Question

8.3 simplify rational exponents (homework) score: 7.05/25 answered: 8/25 question 9 rewrite using a rational exponent. assume all variables are positive. (c^{14}x^{56})^{\frac{1}{7}}= question help: video written example submit question jump to answer

Explanation:

Step1: Apply power - of - a - product rule

According to the rule $(ab)^n=a^n b^n$, we have $(c^{14}x^{56})^{\frac{1}{7}}=c^{14\times\frac{1}{7}}x^{56\times\frac{1}{7}}$.

Step2: Calculate the exponents

$14\times\frac{1}{7} = 2$ and $56\times\frac{1}{7}=8$, so $c^{14\times\frac{1}{7}}x^{56\times\frac{1}{7}}=c^{2}x^{8}$.

Answer:

$c^{2}x^{8}$