# Work out ∛16 as a power of two. (AQA GCSE Higher paper 2017, Q24b)

When you're working with fractional indices, I find the following rhyme really useful:"Fractional indices are like a flower: the bottom's the root, the top's the power".We have a cube root here, which tells us that our root (3) is going to go on the bottom of our fraction, with 1 on the top because the expression is not raised to a power.So first off we convert "cube root 16" to 16 ^1/3 so that we've got our fractional index. So now we can refer to what the question is asking us: to give our answer as a power of 2.We recognize 16 as 2^4 (2x2x2x2), which means we can rewrite what we've got in the following form, using brackets to make everything clearer:16^1/3 = (2^4)^1/3Now recall the rules of indices. We know that when we have a number to a power raised to a second power (as above), we need to multiply the two powers together to get the final answer. So...16^1/3 = 2^(4 x 1/3)= 2^(4/3)

Answered by Ruth D. Maths tutor

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