GCSEMathsEdexcelHigherExam Questions2. AlgebraAlgebraic Roots & Indices

Algebraic Roots & Indices (Edexcel GCSE Maths: Higher)

Exam Questions

2 hours49 questions
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Hard
1
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Simplify      open parentheses m to the power of negative 2 end exponent close parentheses to the power of 5

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2a
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Simplify   m to the power of 5 space divided by space m cubed

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2b
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Simplify    5 x to the power of 4 y cubed space cross times space x squared y

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3a
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Simplify    m to the power of 5 space cross times space m cubed

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3b
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Simplify      p to the power of 6 over p squared

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4a
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Simplify      p squared space cross times space p to the power of 5

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4b
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Simplify      g to the power of 6 space divided by space g to the power of 4

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4c
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Simplify       open parentheses k cubed close parentheses squared

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5
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Simplify    t to the power of 8 space divided by space t cubed

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6a
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Simplify      open parentheses t cubed close parentheses squared

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6b
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Simplify     w to the power of 9 over w to the power of 4

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7
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Simplify  left parenthesis 3 x squared space y right parenthesis to the power of 0

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8
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Simplify  x to the power of 9 over x squared

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9
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Write down the value of g to the power of 0

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10
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Simplify  e to the power of 8 divided by e squared

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11
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Simplify w to the power of 1 space cross times space w to the power of 0 Circle your answer.

1

0

w

w squared

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12
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Given that y to the power of 18 space divided by space y to the power of 6 space equals space y to the power of k , find the value of k.

k = ...................

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13
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Simplify.

a to the power of 6 space divided by space a squared

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14
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Simplify.

open parentheses b to the power of 5 close parentheses cubed

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15
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Simplify.

fraction numerator 3 y cubed over denominator y to the power of negative 4 end exponent end fraction

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1
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Simplify     5 u squared w to the power of 4 space cross times space 7 u w cubed

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2
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Simplify     open parentheses 9 x to the power of 8 y cubed close parentheses to the power of 1 half end exponent

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3a
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Simplify       a to the power of 4 space cross times space a to the power of 5

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3b
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Simplify           fraction numerator 45 e to the power of 6 f to the power of 8 over denominator 5 e f squared end fraction

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3c
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Write down the value of   9 to the power of 1 half end exponent

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4a
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Simplify        x to the power of 7 space cross times space x cubed

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4b
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Simplify       open parentheses m to the power of 4 close parentheses cubed

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4c
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Simplify    fraction numerator 36 a f to the power of 8 over denominator 12 a to the power of 5 f squared end fraction

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5
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Simplify      open parentheses 3 x squared y to the power of 4 close parentheses cubed

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6a
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Simplify      open parentheses p cubed close parentheses squared

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6b
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Simplify     t to the power of 8 over t cubed

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6c
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2 cubed space cross times space 2 to the power of n space equals space 2 to the power of 9

Work out the value of n.

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6d
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2 x cubed space equals space 128

Work out the value of x.

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7
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Simplify fully    fraction numerator p cubed space cross times space p to the power of 4 over denominator p squared end fraction

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8a
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Solve     3 x squared space equals space 147

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8b
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Work out the value of 2 to the power of negative 3 end exponent

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8c
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Simplify    open parentheses 3 x squared close parentheses cubed

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8d
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w space equals space 4 p space minus space 16

Make p spacethe subject of this formula.

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9
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Simplify       2 a cubed b space cross times space 5 a squared b cubed

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10
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Simplify fully    fraction numerator n to the power of 7 space cross times space n cubed over denominator n to the power of 6 end fraction

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11a
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Simplify    m cubed space cross times space m to the power of 4

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11b
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Simplify     open parentheses 5 n p cubed close parentheses cubed

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11c
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Simplify       fraction numerator 32 q to the power of 9 r to the power of 4 over denominator 4 q cubed r end fraction

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12
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Simplify  left parenthesis 2 x cubed y to the power of 5 space right parenthesis to the power of 4

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13
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Simplify   left parenthesis 16 e to the power of 10 space f to the power of 6 space right parenthesis to the power of 1 half end exponent

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14
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Simplify fully.

fraction numerator 3 a to the power of 8 cross times 2 a to the power of 5 over denominator a squared end fraction

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15
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Show that a to the power of 5 cross times space open parentheses a cubed close parentheses squared can be expressed as a to the power of 11.

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1
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16 to the power of 1 fifth end exponent space cross times space 2 to the power of x space equals space 8 to the power of 3 over 4 end exponent

Work out the exact value of x.

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2a
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p cubed space cross times space p to the power of x space equals space p to the power of 9

Find the value of x.

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2b
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open parentheses 7 squared close parentheses to the power of y space equals space 7 to the power of 10

Find the value of y.

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2c
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100 to the power of a space cross times space 1000 to the power of b can be written in the form 10 to the power of w

Show that w space equals space 2 a space plus space 3 b

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3a
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Simplify fully    open parentheses 3 e close parentheses to the power of 0

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3b
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Simplify fully      open parentheses fraction numerator 64 x to the power of 6 over denominator 25 y squared end fraction close parentheses to the power of negative 1 half end exponent

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4
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Given that  open parentheses cube root of 1 over x end root close parentheses to the power of 4 equals x to the power of m

find the value of m

m = .................................................

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5
Sme Calculator2 marks

Given that  fraction numerator 7 to the power of 206 cross times 7 to the power of m over denominator 7 to the power of 214 end fraction equals 7 to the power of negative 3 end exponent

find the value of m

m = ..............................................

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6
Sme Calculator3 marks

Simplify completely      open parentheses fraction numerator 16 w to the power of 8 over denominator y to the power of 20 end fraction close parentheses to the power of begin inline style negative 3 over 4 end style end exponent

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7
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Given that  n to the power of open parentheses negative 4 over 5 close parentheses end exponent equals open parentheses 1 half close parentheses to the power of 4 where n greater than 0

find the value of n.

n space= .............................................

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8
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Given that  fraction numerator y to the power of 5 space cross times space y to the power of n over denominator y to the power of 6 end fraction equals y to the power of 13

work out the value of n.

n space equals space...........................................

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9
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Simplify fully  open parentheses fraction numerator 9 t to the power of 4 w to the power of 9 over denominator 18 t to the power of 6 w to the power of 10 end fraction close parentheses to the power of negative 2 end exponent

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10
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Given that  4 to the power of k plus 3 space end exponent equals space 16 cross times 2 to the power of k

find the value of k.
Show your working clearly.

k = .................................................

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11
Sme Calculator3 marks

Write 27 cross times open parentheses 3 squared close parentheses to the power of 7 as a single power of 3

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12
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Write 16 space cross times space 8 to the power of 2 x end exponent as a power of 2 in terms of x

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13
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The nth term of a sequence is  4 left parenthesis 2 to the power of n space plus space 2 to the power of n minus 1 end exponent right parenthesis

Circle the expression that is equivalent to 4 left parenthesis 2 to the power of n space plus space 2 to the power of n minus 1 end exponent right parenthesis

2 to the power of n plus 2 end exponent space plus space 2 to the power of n plus 1 end exponent

2 to the power of 2 n end exponent space plus space 2 to the power of 2 open parentheses n minus 1 close parentheses end exponent

8 to the power of n space plus space 8 to the power of n minus 1 end exponent

2 to the power of n plus 2 end exponent space plus space 2 to the power of n minus 1 end exponent

 

 

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14
Sme Calculator3 marks

Simplify fully   fraction numerator a cubed b squared over denominator c d end fraction cross times fraction numerator c over denominator a b to the power of 5 end fraction

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15
Sme Calculator4 marks

square root of 6 squared plus 8 squared end root space equals space cube root of 125 a cubed end root

Work out the value of a.

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16
Sme Calculator2 marks

open parentheses a r to the power of b close parentheses to the power of 4 equals 16 r to the power of 20  where a and b are positive integers.

Work out a and b

a equals...................... b equals......................

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17a
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Simplify.

4 a to the power of 1 half end exponent cross times 3 a squared

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17b
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open square brackets fraction numerator 2 a squared over denominator a to the power of negative 3 end exponent end fraction close square brackets cubed

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18
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Show that cube root of a to the power of 4 space end root cross times 1 over a  can be expressed as a to the power of 1 third end exponent.

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19
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Show that  open parentheses a cubed close parentheses to the power of negative 1 third end exponent cross times open parentheses a squared close parentheses to the power of 1 half end exponent equals 1.

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