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

17438 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

The area of a square is 49cm^2. The perimeter of this square is equal to the circumference of a circle. Calculate the radius of the circle to 1 decimal place.


Find where the equation y = x^2 + x - 2 crosses the x-axis.


2^6*2^10=?


How do you solve simultaneous equations?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences