Question

$\frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}$ can be written as

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

Answer 1

Answer: (A), (D)

$5^{-4}$

$5\times 5\times 5\times 5$ can be exponentially written as $5^4$ since 5 is mutiplied with itself four times.
So, $\frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}=\frac{1}{5^4}$

But, we know, for any non-zero integer 'a',
$a^{-m}=\frac{1}{a^m}$, where 'm' is a positive integer.
$⟹\frac{1}{5^4}=5^{-4}$

$\therefore \frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}=\frac{1}{5^4}=5^{-4}$