Question

8.3 simplify rational exponents (homework) score: 9.05/25 answered: 10/25 question 11 rewrite using a rational exponent. assume all variables are positive. $sqrt8{c^{7}b^{7}}=$ question help: video written example

Explanation:

Step1: Recall radical - exponent rule

The rule for converting a radical $\sqrt[n]{a}$ to a rational - exponent is $\sqrt[n]{a}=a^{\frac{1}{n}}$, and for a product inside the radical $\sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}$. So, $\sqrt[8]{c^{7}b^{7}}=(c^{7}b^{7})^{\frac{1}{8}}$.

Step2: Apply power - of - a - product rule

The power - of - a - product rule $(ab)^m = a^m\cdot b^m$. Applying this to $(c^{7}b^{7})^{\frac{1}{8}}$, we get $c^{7\times\frac{1}{8}}b^{7\times\frac{1}{8}}=c^{\frac{7}{8}}b^{\frac{7}{8}}$.

Answer:

$c^{\frac{7}{8}}b^{\frac{7}{8}}$