Solve: $\frac{2^3}{2^{3}.5^{3}}$.

Given: $\frac{2^3}{2^{3}.5^{3}}$.

To do: To solve: $\frac{2^3}{2^{3}.5^{3}}$.

Solution:

$\frac{2^3}{2^{3}.5^{3}}$

$=2^3\times2^{-3}\times5^{-3}$                       [$\because \frac{1}{a^m}=a^{-m}$]

$=2^{3-3}\times5^{-3}$                               [$\because a^m\times a^n=a^{m+n}$]

$=2^0\times 5^{-3}$

$=1\times\frac{1}{5^3}$

$=\frac{1}{5\times5\times5}$

$=\frac{1}{125}$

Thus, $\frac{2^3}{2^{3}.5^{3}}=\frac{1}{125}$

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Updated on: 10-Oct-2022

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