Laws of Indices & Surds (AQA AS Maths: Pure)

Write down the value of 

Use your answer to part (a) to show that .

Given that , find the value of a.

Simplify 

Simplify the following expressions:

Given that , express each of the following in the form , where a and n are constants.

Simplify 

By expanding and simplifying, show that

Give an example to show that  is not true in general.

Show that .

Solve the equation  , giving your answer in the form where a and b are integers.

A rectangle has an area of 14 m² and a length of m.  Find the width of the rectangle, showing clear algebraic working. Give your answer as an exact value.

Show that   can be written as .

Given that , find the value of a.

Show that   can be written as , where a and b are rational numbers to be found.

Write down the value of .

Use your answer to part (a) to show that 

Given that , find the value of a.

Simplify 

Simplify the following expressions, giving your answers in the form  where  and  are rational numbers and any fractions are in lowest terms.

Given that , express each of the following in the form , where a and b are constants.

Show that  

By expanding and simplifying, show that

 is not true in general. Give an example of an a and a b for which it is true.

Show that  , where a and b are rational numbers to be found.

Solve the equation , giving your answer in the form  where a and b are integers.

The two parallel sides of a trapezium have lengths of  cm and  cm, and the area of the trapezium is  cm².   Showing clear algebraic working, determine the perpendicular distance between the two parallel sides of the trapezium.  Give your answer in the form  where a and b are integers.

Show that   can be written as .

Show that , where a is a rational number to be found.

Show that    can be written as , where and a and b are integers to be found.

Write down the value of 

Use your answer to part (a) to show that .

Given that , find the possible values of a.

Simplify 

Simplify the following expressions, giving your answers in the form where a and n are rational numbers and any fractions are in lowest terms.

Given that , express each of the following in the form , where a and n are constants.

Show that , where a and b are integers.

By expanding and simplifying, show that

 is not true in general. Give an example of an a and a b for which it is true.

Show that   , where a and b are rational numbers.

Solve the equation  

Expand .

A square has an area of  m² and a side length of   m.

Show that , and explain why this proves that a and b must both be non-negative.

Show that .

By using the substitution  or otherwise, solve the equation  .  Hence determine the side length of the square.