Question

1. SIMPLIFY:-
QUESTION :- (25)^-1/3 * ³√16

Answer 1

Dear student

$$\begin{gathered} {\left(25\right)}^{\frac{-1}{3}}\times \sqrt[3]{16} \\ ={\left(\frac{1}{25}\right)}^{\frac{1}{3}}\times {16}^{\frac{1}{3}}\left[\mathrm{As}{\mathrm{a}}^{-\mathrm{m}}=\frac{1}{{\mathrm{a}}^{\mathrm{m}}}\right] \\ ={\left(25\times 16\right)}^{\frac{1}{3}}\left[\mathrm{As}{\mathrm{a}}^{\mathrm{m}}\times {\mathrm{b}}^{\mathrm{m}}={\left(\mathrm{a}\times \mathrm{b}\right)}^{\mathrm{m}}\right] \\ ={400}^{\frac{1}{3}} \\ ={\left(2\times 2\times 2\times 2\times 5\times 5\right)}^{\frac{1}{3}} \\ =2{\left(50\right)}^{\frac{1}{3}} \end{gathered}$$
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