What you need to know

Things to remember:

  • When we put an exponent on a fraction, we can just put the exponent on the top and bottom numbers.

An exponent is a number written to the top right of a number and tells us how many times we multiply a number by itself.

6^2 = 6\times 6

6^3 = 6\times 6\times 6

6^4= 6\times 6\times 6\times 6

So, all we’re doing when we have exponents is lots of multiplications. When we do these multiplications, we refer to it as “evaluating the exponent”.

Evaluate the following exponents:





This topic will focus on fractions with powers, meaning we will be multiplying lots of fractions, which we do by multiplying the tops and multiplying the bottoms.



We can use all these facts to help us evaluate exponents with fractional bases.

Evaluate \left(\frac{2}{7}\right)^3

We know that when we have a power of 3, we multiply the number by itself 3 times. This is the same with fractions.

\left(\frac{2}{7}\right)^3 =\frac{2}{7}\times\frac{2}{7}\times \frac{2}{7}

But, we know that we just multiply the tops and bottoms.


And now, we can just do these multiplications.



If we look back a step, we can learn an important fact:


We can write these multiplications as powers.


So, when we have an exponent on a fraction, it is the same as putting that exponent on both numbers in the fraction.




Example Questions

Question 1: Evaluate \left(\dfrac{1}{6}\right)^3



Question 2: Evaluate \left(\dfrac{5}{2}\right)^2