Question

question 4 (1 point) (03.01 lc) rewrite the expression with a rational exponent as a radical expression. 1 4 2 5 4 a b c d 4 4 4 4 2 5 10

Explanation:

Step1: Recall radical - exponent rule

The rule for converting a rational exponent to a radical is $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$, where $a$ is the base, $m$ is the numerator of the exponent and $n$ is the denominator of the exponent.

Step2: Analyze the given rational exponent

We are given the rational - exponent expression $4^{\frac{5}{2}}$. Here, $a = 4$, $m = 5$ and $n = 2$.

Step3: Apply the rule

Using the rule $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$, we get $\sqrt[2]{4^{5}}$. Since the index $n = 2$, we can write it as $\sqrt{4^{5}}$.

Answer:

$\sqrt{4^{5}}$