Question

8.3 simplify rational exponents (homework) score: 22.05/25 answered: 23/25 question 24 simplify. assume all variables are positive. (16c^(20/3)z^(8/3))^(3/4)= question help: video written example submit question jump to answer

Explanation:

Step1: Apply power - of - a - product rule

$(ab)^n=a^n\times b^n$. So, $(16c^{\frac{20}{3}}z^{\frac{8}{3}})^{\frac{3}{4}} = 16^{\frac{3}{4}}\times(c^{\frac{20}{3}})^{\frac{3}{4}}\times(z^{\frac{8}{3}})^{\frac{3}{4}}$

Step2: Simplify $16^{\frac{3}{4}}$

$16^{\frac{3}{4}}=(2^4)^{\frac{3}{4}} = 2^{4\times\frac{3}{4}}=2^3 = 8$

Step3: Simplify $(c^{\frac{20}{3}})^{\frac{3}{4}}$

Using the power - of - a - power rule $(a^m)^n=a^{mn}$, we have $(c^{\frac{20}{3}})^{\frac{3}{4}}=c^{\frac{20}{3}\times\frac{3}{4}}=c^5$

Step4: Simplify $(z^{\frac{8}{3}})^{\frac{3}{4}}$

Using the power - of - a - power rule $(a^m)^n=a^{mn}$, we get $(z^{\frac{8}{3}})^{\frac{3}{4}}=z^{\frac{8}{3}\times\frac{3}{4}}=z^2$

Step5: Combine the results

$8c^5z^2$

Answer:

$8c^5z^2$