Question

8.3 simplify rational exponents (homework)
score: 12.05/25 answered: 13/25
question 14
rewrite without negative or fractional exponents.
$\frac{6}{11}z^{-\frac{2}{7}}=square$
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Explanation:

Step1: Apply negative - exponent rule

Recall that $a^{-n}=\frac{1}{a^{n}}$. So, $z^{-\frac{2}{7}}=\frac{1}{z^{\frac{2}{7}}}$. Then the expression $\frac{6}{11}z^{-\frac{2}{7}}$ becomes $\frac{6}{11}\times\frac{1}{z^{\frac{2}{7}}}=\frac{6}{11z^{\frac{2}{7}}}$.

Step2: Rewrite fractional - exponent as a root

Recall that $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$. So, $z^{\frac{2}{7}} = \sqrt[7]{z^{2}}$.
The final non - negative and non - fractional form is $\frac{6}{11\sqrt[7]{z^{2}}}$.

Answer:

$\frac{6}{11\sqrt[7]{z^{2}}}$