Question

Simplify the following using law of exponents. $\left(3^2\right)\times (3^2{)}^4$

• A. $3^{10}$
• B. $3^{25}$
• C. $3^5$
• D. $3^6$

Answer 1

The correct option is A $3^{10}$

Given $\left(3^2\right)\times (3^2{)}^4=3^2\times 3^{2\times 4}$ [$\because (a^m{)}^n=a^{mn}$]
$=3^2\times 3^8$
we know that $a^m\times a^n=a^{m+n}$
$\Rightarrow 3^2\times 3^8=3^{2+8}$
$\therefore \left(3^2\right)\times (3^2{)}^4=3^{10}$