Exponents and fractions

In this lesson, we solve problems involving both exponents and fractions.

As we have already learnt, if a number or variable is repeatedly multiplied with itself, it is expressed as a number with an exponent.

For example, $5 \times 5 \times 5 = 5^{3}$ and $a \times a \times a \times a \times a = a^{5}$

Consider the following problems involving exponents and fractions.

Evaluate $\frac{3^{2}}{5}$

Solution

Step 1:

Here the exponent 2 applies only to the numerator 3 of the fraction.

Step 2:

$\frac{3^{2}} = 9$ and therfore

$\frac{3^{2}}{5} = \frac{9}{5}$

Evaluate $\left (\frac{4}{5}\right )^3$

Solution

Step 1:

Here the exponent 3 applies to the entire fraction $\frac{4}{5}$.

Step 2:

So, $\left (\frac{4}{5}\right )^3 = \frac{4}{5} \times \frac{4}{5} \times \frac{4}{5} \times = \frac{64}{125}$and therefore

$\left (\frac{4}{5}\right )^3 = \frac{64}{125} $