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 multipped with itself, it is expressed as a number with an exponent.

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

Consider the following problems involving exponents and fractions.

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

Solution

Step 1:

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

Step 2:

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

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

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

Solution

Step 1:

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

Step 2:

So, $left (frac{4}{5} ight )^3 = frac{4}{5} imes frac{4}{5} imes frac{4}{5} imes = frac{64}{125}$and therefore

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