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8.3 simplify rational exponents (homework)
score: 8.05/25 answered: 9/25
question 10
rewrite using a rational exponent. assume all variables are positive.
\\(\sqrt4{z^{3}}=\\)
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Explanation:

Step1: Recall radical - exponent rule

The rule for converting a radical $\sqrt[n]{a^m}$ to a rational - exponent form is $a^{\frac{m}{n}}$. Here, $n = 4$ (the index of the radical) and $m = 3$ (the exponent of the base inside the radical), and the base $a=z$.

Step2: Apply the rule

Using the rule $\sqrt[n]{a^m}=a^{\frac{m}{n}}$, we can rewrite $\sqrt[4]{z^{3}}$ as $z^{\frac{3}{4}}$.

Answer:

$z^{\frac{3}{4}}$