Question

Find the value of x if $\frac{8^2}{5^6}={\left(\frac{x}{5}\right)}^6$

• A. 4
• B. 8
• C. 2
• D. 16

Answer 1

The correct option is C

2

We know that $8=2^3$

$8^2={\left(2^3\right)}^2=2^6$ $[\because {\left(a^m\right)}^n=a^{mn}]$

$\frac{8^2}{5^6}=\frac{2^6}{5^6}=(\frac{2}{5}{)}^6$ $[\because \frac{a^m}{b^m}={\left(\frac{a}{b}\right)}^m]$

Given that, $\frac{8^2}{5^6}={\left(\frac{x}{5}\right)}^6$

$\Rightarrow {\left(\frac{2}{5}\right)}^6={\left(\frac{x}{5}\right)}^6$

$\Rightarrow \frac{2}{5}=\frac{x}{5}$

$\Rightarrow x=2$