Simplify (25)^-1/3X 3 root of 16

Open in App

Solution

${(25)}^{\frac{- 1}{3}} \times \sqrt[3]{16} = \frac{1}{{(25)}^{\frac{1}{3}}} \times \sqrt[3]{2 \times 2 \times 2 \times 2} {Since a^{- m} = \frac{1}{a^{m}}} = \frac{2 \sqrt[3]{2}}{\sqrt[3]{25}} = \frac{2 \sqrt[3]{2}}{\sqrt[3]{25}} \times \frac{\sqrt[3]{5}}{\sqrt[3]{5}} = \frac{2 \sqrt[3]{10}}{\sqrt[3]{125}} = \frac{2}{5} \sqrt[3]{10}$

Suggest Corrections

Similar questions

\begin{matrix} i) (\sqrt{5})^{- 3} (\sqrt{2})^{- 3} i i) \frac{1}{\sqrt[3]{4^{- 5}}} i i i) (25)^{- 1 / 3} \times \sqrt[3]{16} i v) (\sqrt[3]{8})^{- 1 / 2} \end{matrix}

Simplify: ${(\frac{81}{16})}^{\frac{- 3}{4}} \times {(\frac{25}{9})}^{\frac{- 3}{2}}$

(81 / 16)^{- 3 / 4} \times [(25 / 9)^{- 3 / 2} \div (5 / 2)^{- 3}]

{(\frac{81}{16})}^{\frac{- 3}{4}} \times ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ {(\frac{25}{9})}^{\frac{- 3}{2}} \div {(\frac{5}{2})}^{- 3} ⎫ ⎪ ⎪ ⎬ ⎪ ⎪ ⎭

{(\frac{81}{16})}^{- 3 / 4} \times {(\frac{25}{9})}^{- 3 / 2} \times {(\frac{2}{5})}^{- 3}

Join BYJU'S Learning Program