Which of the following expressions is equal to $5^{2} \times 3^{2} ?$

15^{2}

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15^{4}

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5^{4}

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3^{4}

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Solution

The correct option is A $15^{2}$
The expression $5^{2} \times 3^{2}$ involves the multiplication of exponents with different bases $(5, 3)$ but same exponent, $2.$

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

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

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Similar questions

Question 21

Which of the following is not true?
(a) $3^{2} > 2^{3}$
(b) $4^{3} = 2^{6}$
(c) $3^{3} = 9$
(d) $2^{5} > 5^{2}$

{(\frac{2}{5})}^{2}

{(2^{- 3})}^{2}

5^{2} \times 5^{3}

{[{(- \frac{2}{5})}^{- 1}]}^{- 2}

The value of expression $12^{2} \times 5^{2}$ is equal to

The value of expression $6^{2} \times 5^{2}$ is equal to

{(\frac{5}{3})}^{- 6} \times {(\frac{3^{2}}{5^{2}})}^{- 2}

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