Question

evaluate (27/125)^⅔ × (243)^-⅖​

Answer 1

Answer:

$( \frac{27}{125} ) {}^{ \frac{3}{2} } \times (243) {}^{ \frac{ 5}{ - 2} } \\ ( \frac{3}{5} ) {}^{2} \times (3) {}^{ - 2} \\ \frac{9}{25} \times 3 = \frac{27}{25}$

ok

Answer 2

Answer:

Required value of the given term is

$\frac{ {3}^{ \frac{ - 4}{3} } }{25}$

Step-by-step explanation:

Given,

${ (\frac{27}{125} )}^{ \frac{2}{3} } \times {(243)}^{ - \frac{2}{3} }$

This is a problem of power of indices.

${ (\frac{3 \times 3 \times 3}{5 \times 5 \times 5} )}^{ \frac{2}{3} } \times {(3 \times 3 \times 3 \times 3 \times 3)}^{ - \frac{2}{3} }$

${ (\frac{ {3}^{3} }{ {5}^{5} } )}^{ \frac{2}{3} } \times {( {3}^{5} )}^{ - \frac{2}{3} }$

$\frac{ { {(3)}^{(3)} }^{ \frac{2}{3} } }{ { {(5)}^{(3)} }^{ \frac{2}{3} } } \times { {3}^{(5)} }^{ - \frac{2}{3} }$

$\frac{ {3}^{3 \times \frac{2}{3} } }{ {5}^{3 \times \frac{2}{3} } } \times {3}^{5 \times ( - \frac{2}{3}) } \\ \frac{ {3}^{2} }{ {5}^{2} } \times {3}^{ - \frac{10}{3} }$

$\frac{ {3}^{2} \times {3}^{ - \frac{10}{3} } }{25}$

$\frac{ {3}^{2 - \frac{10}{3} } }{25} \\ \frac{ {3}^{ \frac{ - 4}{3} } }{25}$

Here applied formulas are

${x}^{ - y} = \frac{1}{ {x}^{y} }$

${x}^{y} \times {x}^{z} = {x}^{y + z}$

${x}^{ {y}^{a} } = {x}^{y \times a}$