Question

find the value of (243/32)^3/5×(2/3)^-3×[(125/27)^2/3]

Answer 1

I hope u can understand

Answer 2

Answer: The value of the expression is $\frac{2025}{64}$.

Explanation:

The given expression is,

$(\frac{243}{32})^{\frac{3}{5}}\times (\frac{2}{3})^{-3}\times(\frac{125}{27})^{\frac{2}{3}}$

Use $a^{mn}=(a^m)^n$

$((\frac{243}{32})^{\frac{1}{5}})^3\times (\frac{2}{3})^{-3}\times((\frac{125}{27})^{\frac{1}{3}})^2$

Use $a^{-n}=\frac{1}{a^n}$

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

Use $a^{m+n}=a^ma^n$

$(\frac{3}{2})^6\times(\frac{5}{3})^2$

$\frac{3^6}{2^6}\times\frac{5^2}{3^2}$

Use $a^{m-n}=\frac{a^m}{a^n}$

$\frac{3^4}{2^6}\times5^2$

$\frac{2025}{64}$

Therefore, the value of the expression is $\frac{2025}{64}$.