which exponential expression is equivalent to $sqrt3{5^{2}}$? a $5^{\frac{3}{2}}$ b $5^{\frac{2}{3}}$ c…

which exponential expression is equivalent to $sqrt3{5^{2}}$? a $5^{\frac{3}{2}}$ b $5^{\frac{2}{3}}$ c $5^{\frac{1}{6}}$ d $5^{\frac{1}{3}}$ e $5^{\frac{1}{2}}$

which exponential expression is equivalent to $sqrt3{5^{2}}$? a $5^{\frac{3}{2}}$ b $5^{\frac{2}{3}}$ c $5^{\frac{1}{6}}$ d $5^{\frac{1}{3}}$ e $5^{\frac{1}{2}}$

Answer

Explanation:

Step1: Recall radical - exponent rule

The rule for converting a radical $\sqrt[n]{a^m}$ to an exponential form is $a^{\frac{m}{n}}$. Here, $a = 5$, $m = 2$, and $n=3$ for the expression $\sqrt[3]{5^{2}}$.

Step2: Write the equivalent exponential form

Using the rule $\sqrt[n]{a^m}=a^{\frac{m}{n}}$, we get $5^{\frac{2}{3}}$.

Answer:

B. $5^{\frac{2}{3}}$