Simplify : (2^5 )^2 7^3 8^3 7 - Vidyadip

Question

Simplify :
$\frac{\left(2^5\right)^2 \times 7^3}{8^3 \times 7}$

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Answer

We have,
$\frac{\left(2^5\right)^2 \times 7^3}{8^3 \times 7}=\frac{2^{5 \times 2} \times 7^3}{\left(2^3\right)^3 \times 7}$ $\left[\because 8=2 \times 2 \times 2=2^3\right.$ and $\left.\left(a^m\right)^n=a^{m n}\right]$
$=\frac{2^{10} \times 7^3}{2^9 \times 7^1}=2^{10-9} \times 7^{3-1}$ $\left[\because a^m \div a^n=a^{m-n}\right]$
$=2^1 \times 7^2=2 \times 7^2=2 \times 7 \times 7=98$

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