Question

Expand ${\left(\frac{4}{5}\right)}^3$ and write in exponent form.

Answer 1

As we know for any non-zero integers $\text{'}a\text{'}$ and $\text{'}b\text{'}$ and for any natural number $\text{'}n\text{'}$, $\frac{a^n}{b^n}={\left(\frac{a}{b}\right)}^n$.

So, ${\left(\frac{4}{5}\right)}^3$ is in the form of ${\left(\frac{a}{b}\right)}^n$ only, thus, we can write exponent individually on each base, i.e., ${\left(\frac{4}{5}\right)}^3$$=\left(\frac{4^3}{5^3}\right)$.

Hence, ${\left(\frac{4}{5}\right)}^3$$=\left(\frac{4^3}{5^3}\right)$ in the expanded form.