Question

what is \\(\sqrt{a^8}\\) in simplest fractional (rational) exponent?\
\\(a^4\\)\
\\(a^8\\)\
\\(a^2\\)\
\\(a^{16}\\)\
rewatch skip

Explanation:

Step1: Recall the radical to exponent rule

The rule for converting a square root to a rational exponent is $\sqrt[n]{x^m}=x^{\frac{m}{n}}$. For a square root, $n = 2$, so $\sqrt{x^m}=x^{\frac{m}{2}}$.

Step2: Apply the rule to $\sqrt{a^8}$

Using the rule with $x = a$ and $m = 8$, we have $\sqrt{a^8}=a^{\frac{8}{2}}$.

Step3: Simplify the exponent

Simplify $\frac{8}{2}$ to get $4$. So $a^{\frac{8}{2}}=a^4$.

Answer:

A. $a^4$