Question

Simplify the following:
${(-5)}^4\times {(-5)}^{-6}$

• A. $\frac{1}{25}$
• B. $\frac{1}{5}$
• C. $\frac{-1}{25}$
• D. None of these

Answer 1

The correct option is A $\frac{1}{25}$

we know that,

$\because a^m\ast a^n=a^{m+n}$

and

$\because \frac{1}{a^m}=a^{-m}$

${(-5)}^4\times {(-5)}^{-6}$

$=(-5{)}^{-6+4}$

$=(-5{)}^{-2}$

$=\frac{1}{(-5{)}^2}$

$=\frac{1}{25}$