Question

find the multiplicative inverse of (125/27)^-2/3

Answer 1

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Answer 2

Answer:  $\dfrac{25}{9}$

Step-by-step explanation:

Multiplicative inverse of any number is the reciprocal of the number.

Given expression : $(\dfrac{125}{27})^{\dfrac{-2}{3}}$

$=(\dfrac{5^3}{3^3})^{\dfrac{-2}{3}}\\\\=\dfrac{5^{\dfrac{-2\times3}{3}}}{3^{\dfrac{-2\times3}{3}}}\\\\=\dfrac{5^{-2}}{3^{-2}}=\dfrac{3^2}{5^2}=\dfrac{9}{25}$

Multiplicative inverse of $(\dfrac{125}{27})^{\dfrac{-2}{3}}$ will be

$\dfrac{1}{\dfrac{9}{25}}=\dfrac{25}{9}$