Question

Simplify 25 raise to the power-1/3 multiplied by 16 root 3

Answer 1

Hey here is your answer

Answer 2

$Given \: 25^{\frac{-1}{3}} \times 16\sqrt{3}$

$= \frac{1}{25^{\frac{1}{3}}} \times 16\sqrt{3}$

$\boxed {\pink { Since, a^{-n} = \frac{1}{a^{n}} }}$

$= \frac{16\sqrt{3}}{(5^{2})^{\frac{1}{3}}}$

$= \frac{16\sqrt{3}}{(5)^{\frac{2}{3}}}$

$= \frac{16\sqrt{3}\times 5^{\frac{1}{3}}}{5^{\frac{1}{3}} \times (5)^{\frac{2}{3}}}$

$= \frac{16\sqrt{3}}{5^{\frac{1}{3}+ \frac{2}{3}}}$

$= \frac{16\sqrt{3} \times 5^{\frac{1}{3}}}{5^{\frac{3}{3}}}$

$= \frac{16\sqrt{3} \times 5^{\frac{1}{3}}}{5}$

Therefore.,

$\red {25^{\frac{-1}{3}} \times 16\sqrt{3}}$

$\green{= \frac{16\sqrt{3} \times 5^{\frac{1}{3}}}{5}}$

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