Question

The value of m for which (4/9)^m × (3/2)^-2 = (8/27)^5/3 - it would be amazing if you could answer the questions with the steps.​

Answer 1

Step-by-step explanation:

Hope it helps you☺️

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Answer 2

Hello dear :)

Here's Your solution ☺️⬇️

$\red \maltese \tt \: \bigg( \frac{4}{9} \bigg) ^{m} \times \bigg( \frac{3}{2} \bigg)^{-2} = \bigg( \frac{8}{27} \bigg)^{ \frac{5}{3} }$

Making same base :

$\tt\implies \bigg ( \frac{2}{3} \bigg)^{2m} \times \bigg( \frac{2}{3} \bigg) ^{2 } = \bigg( \frac{2}{3} \bigg) ^{\cancel3 \times \frac{5}{\cancel3}}$

Now, equating the powers :

$\tt \implies { 2m + 2} = {5}$

$\implies\tt 2m = 5 - 2 \\ \\ \tt 2m = 3$

$\boxed{ \tt\red{ \therefore \: m = \frac{3}{2} }}$

Hence, we got the value of this question.

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$\sf \red{Something\: Important}$☺️

• We do reciprocal of the fraction then the power sign is changed.

• 4/9 can become (2/3)^2 as $\sf{ 2 \times 2 = 4 \: \blue{and} \: 3 \times 3 = 9}$ In this way (2/3)^2m

• Now it's clear for you I think (◕ᴗ◕✿)

Hope this helps you :) ❤️

Have a great day!! ⭐