Question

8.3 simplify rational exponents (homework) score: 17.05/25 answered: 18/25 question 19 simplify using rational exponents. you do not need to expand powers of integers. (4c^(2/5))^(9/2)= question help: video written example

Explanation:

Step1: Apply power - of - a - product rule

$(4c^{\frac{2}{3}})^{\frac{9}{2}}=4^{\frac{9}{2}}\times(c^{\frac{2}{3}})^{\frac{9}{2}}$

Step2: Simplify $4^{\frac{9}{2}}$

$4^{\frac{9}{2}}=(4^{\frac{1}{2}})^9 = 2^9=512$

Step3: Simplify $(c^{\frac{2}{3}})^{\frac{9}{2}}$

Using the power - of - a - power rule $(a^m)^n=a^{mn}$, we have $(c^{\frac{2}{3}})^{\frac{9}{2}}=c^{\frac{2}{3}\times\frac{9}{2}}=c^3$

Step4: Combine the results

$4^{\frac{9}{2}}\times(c^{\frac{2}{3}})^{\frac{9}{2}} = 512c^3$

Answer:

$512c^3$