Question

Which of the following expression is equal to $5^2\times 3^2?$

• A. ${15}^4$
• B. ${15}^4$
• C. $3^4$
• D. ${15}^2$

Answer 1

The correct option is D ${15}^2$

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

The expression $5^2\times 3^2$ involves the multiplication of exponents with different bases $(5,3)$ but same exponent $\left(2\right)$.

$\bullet$ Rule for the multiplication of exponents with different bases but same exponent:
$a^n\times b^n=(a\times b{)}^n=(ab{)}^n$

Following the same rule $a^n\times b^n=(ab{)}^n$ to solve $5^2\times 3^2$, we get
$5^2\times 3^2=(5\times 3{)}^2={15}^2$

$\therefore$ Option (d.) is the correct one.