Question

By what number should $5^2$ be multiplied so that the product is 3125 .

• A. $5^4$
• B. $5^2$
• C. $5^3$
• D. $5^5$

Answer 1

The correct option is C $5^3$

Let the number be $X$.
$⟹5^2\times X=3125$
we can write 3125 as
$\begin{array}{cc}5& 3125\\ 5& 625\\ 5& 125\\ 5& 25\\ 5& 5\\ & 1\end{array}$
$3125=5\times 5\times 5\times 5\times 5=5^5$
Now putting $5^5$ in place of 3125
$⟹5^2\times X=5^5$
$⟹X=\frac{5^5}{5^2}$
Using Laws of Exponents we know that,
$\frac{a^m}{a^n}=a^{m-n}$
$⟹X=\frac{5^5}{5^2}=5^{5-2}=5^3$
So the number to be multiplied by $5^2$ is $5^3$ so that the product is 3125.