Question

Simplify (1/25)^-3/2

Answer 1

125

Answer 2

\(\bf \large {
\left(\cfrac{1}{25}\right)^{-\frac{3}{2}}\implies \left(\cfrac{25}{1}\right)^{+\frac{3}{2}}\implies 25^{\frac{3}{2}}
\\ \quad \\
recall\implies a^{\frac{{\color{blue} n}}{{\color{red} m}}} = \sqrt[{\color{red} m}]{a^{\color{blue} n}} \qquad \qquad

\sqrt[{\color{red} m}]{a^{\color{blue} n}}=a^{\frac{{\color{blue} n}}{{\color{red} m}}}\quad thus
\\ \quad \\
25^{\frac{{\color{blue}{ 3}}}{{\color{red}{ 2}}}}\implies ?
}\)