Question

what is the value of 32 ⅖​

Answer 1

Answer:

answer is 4

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Answer 2

Answer:

One of the laws of indices deals with cases where there are powers and roots at the same time.

x p q = q √ x p = ( q √ x ) p

The denominator shows the root and the numerator gives the power.

Note that the power can be inside or outside the root.

I prefer to find the root first and then raise to the power because this keeps the numbers smaller. They can usually be calculated mentally rather than needing a calculator

32^2/5 = ( 5 √ 32 )^2

= 2^2 ( 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 2 5 = 32 )

= 4

Compare this with the other method of squaring first.

5 √ 32 2 = 5 √ 1024

= 4

While I know that 2^5 = 32, the square of 32 and the fifth root of 1024 are not facts that I would be able to recall from memory.

Hope it helps :)

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