Question

If $a,b$, and $c$ are positive integers such that $a^b=x$ and $c^b=y$, then $xy=$?

• A. ${ac}^b$
• B. ${ac}^{2b}$
• C. ${\left(ac\right)}^b$
• D. ${\left(ac\right)}^{2b}$
• E. ${\left(ac\right)}^{b^2}$

Answer 1

The correct option is C ${\left(ac\right)}^b$

Let $a^b=x$ ....(1)

and $c^b=y$ ....(2)

Now multiplying both the above equations, we get

$a^b.c^b=x\times y$

$xy=(ac{)}^b$

Hence, option C is correct.