Question

Find the value of ${625}^{\raisebox{1ex}{$-3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$

Answer 1

Finding the value of ${625}^{\raisebox{1ex}{$-3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$

We can rewrite it as ${\left(\frac{1}{625}\right)}^{3/4}$

By the law of exponents, we know that ${\mathbf{\left(}{\mathbf{a}}^{\mathbf{m}}\mathbf{\right)}}^{\mathbf{n}}\mathbf{=}{\mathbf{a}}^{\mathbf{m}\mathbf{n}}$

$\begin{array}{rcl}{\left(\frac{1}{625}\right)}^{3/4}& =& {\left({\left(\frac{1}{625}\right)}^{1/4}\right)}^3\\ & =& {\left(\frac{1}{5}\right)}^3\\ & =& \left(\frac{1}{125}\right)\end{array}$

Hence the value of ${625}^{-¾}\mathrm{is}\frac{1}{125}$