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Algebraic Roots & Indices (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

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1
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Simplify a squared divided by a to the power of 6.

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2a
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Simplify space p to the power of 2 space end exponent cross times p to the power of 4 space end exponent.

2b
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Simplify space m to the power of 15 space end exponent divided by m to the power of 5 space end exponent.

2c
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Simplify space open parentheses k cubed close parentheses to the power of 5.

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3
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Simplify.

5 m squared cross times 2 m cubed 

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1
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2 to the power of 3 x plus 1 end exponent equals 8 to the power of 2 minus x end exponent

Find the value of x

x equals.......................

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2
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Simplify.

open parentheses x to the power of 8 y to the power of 7 close parentheses space divided by space open parentheses x to the power of negative 1 end exponent y cubed close parentheses

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3
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Simplify.

open parentheses 27 x to the power of 9 close parentheses to the power of 2 over 3 end exponent

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4
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Simplify left parenthesis 81 y to the power of 16 right parenthesis to the power of 3 over 4 end exponent space.

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5a
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Simplify left parenthesis 3 p squared right parenthesis to the power of 5.

5b
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Simplify 18 x squared y to the power of 6 divided by 2 x y squared.

5c
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Simplify open parentheses 5 over m close parentheses to the power of negative 2 end exponent.

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1
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Simplify.

open parentheses x cubed over 8 close parentheses to the power of negative 4 over 3 end exponent

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2
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Simplify cube root of 27 t to the power of 27 end root.

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3
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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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1
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Simplify open parentheses 256 x to the power of 256 close parentheses to the power of 3 over 8 end exponent.

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2
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cube root of y squared end root equals root index 6 of x and space y equals n-th root of x.  

Find the value of n.  

n equals................................................. 

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3
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x to the power of negative 1 third end exponent equals 32 x to the power of negative 2 end exponent

Find the value of x.

x = ................................................... 

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4
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Simplify open parentheses fraction numerator 16 a to the power of 8 over denominator c to the power of 12 end fraction close parentheses to the power of 3 over 4 end exponent.

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5
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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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