Question

Which among the following would be equal to $3^{-5}\times 3^{-2}$?

• A. $3^7$
• B. $3^{-10}$
• C. $3^{10}$
• D. $3^{-7}$

Answer 1

The correct option is D $3^{-7}$

$\underset{–}{\text{Need to simplify:}}{3}^{-5}\times 3^{-2}$

• Involves the multiplication of exponents with same base $\left(3\right)$ and different powers $(-5,-2),$ which are negative in nature.
• Applying exponent rule, $a^m\times a^n=a^{m+n},$ we get:

$3^{-5}\times 3^{-2}=3^{(-5)+(-2)}$
$⟹3^{-5}\times 3^{-2}=3^{-7}$

$\therefore 3^{-5}\times 3^{-2}$ would be equal to $3^{-7}$.

Hence, option (d.) is the correct choice.