Question

Find the value of (64/25)-3/2

Answer 1

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}

Answer 2

Step-by-step explanation:

64/25-3/2

take lcm

(128-75)/58

=>53/58

i hope it's helpful..

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