Question

$\frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}=?$

• A. $(\frac{1}{5}{)}^{-4}$
• B. $(\frac{1}{5}{)}^{-6}$
• C. $5^{-4}$
• D. $5^{-6}$

Answer 1

The correct option is C $5^{-4}$

We know that $\frac{1}{2}$ can be written as:
$\frac{1}{2}=2^{-1}$
Similarly, $\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=2^{-3}$
In the expression given above, $\frac{1}{5}$ is multiplied by itself 5 times.
Hence, $\frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}=5^{-4}$