Question

Simplify :

${\left(\frac{1}{25}\right)}^4\times {\left(5\right)}^4$.

Answer 1

Given; ${\left(\frac{1}{25}\right)}^4\times {\left(5\right)}^4$.

We know that

${\mathrm{a}}^{\mathrm{m}}\times {\mathrm{b}}^{\mathrm{m}}={\left(\mathrm{ab}\right)}^{\mathrm{m}}$

Now,

${\left(\frac{1}{25}\right)}^4\times {\left(5\right)}^4={\left(\frac{1}{25}\times 5\right)}^4\left[\because {\mathrm{a}}^{\mathrm{m}}\times {\mathrm{b}}^{\mathrm{m}}={\left(\mathrm{ab}\right)}^{\mathrm{m}}\right]$

$$\begin{gathered} ={\left(\frac{1}{{\cancel{25}}^5}\times {\cancel{5}}^1\right)}^4 \\ ={\left(\frac{1}{5}\right)}^4 \\ =\frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}\times \frac{1}{5} \\ =\frac{1}{625} \end{gathered}$$

Hence, value of ${\left(\frac{1}{25}\right)}^4\times {\left(5\right)}^4$ is $\frac{1}{625}$.