Question

find the value of (64/25)^-3/2

Answer 1

FOLLOW ME. HERE UR ANSWER

Answer 2

Answer:

$\left(\frac{64}{25}\right)^{\frac{-3}{2}}$= $\frac{125}{512}$

Explanation:

Given $\left(\frac{64}{25}\right)^{\frac{-3}{2}}$

= $\left(\frac{25}{64}\right)^{\frac{3}{2}}$

/* By Exponential Law :*/

$\boxed{\left(\frac{a}{b}\right)^{-n}=\left(\frac{b}{a}\right)^{n}}$

= $\left(\frac{5^{2}}{8^{2}}\right)^{\frac{3}{2}}$

= $\left(\frac{5}{8}\right)^{2\times\frac{3}{2}}$

/* By Exponential Law :*/

$\boxed {\left(a^{m}\right)^{n}=a^{mn}}$

=$\left(\frac{5}{8}\right)^{3}$

= $\frac{5^{3}}{8^{3}}$

/* By Exponential Law :*/

$\boxed { \left(\frac{a}{b}\right)^{m} = \frac{a^{m}}{b^{m}}}$

= $\frac{5\times5\times5}{8\times8\times8}$

= $\frac{125}{512}$

Therefore,

$\left(\frac{64}{25}\right)^{\frac{-3}{2}}$

= $\frac{125}{512}$