## james1769 one year ago Describe how to transform the quantity of the third root of x to the fourth power, to the fifth power into an expression with a rational exponent. Make sure you respond with complete sentences.

1. Michele_Laino

please keep in mind that the radical: $\sqrt[3]{{{x^4}}}$ can be rewritten as below: ${x^{4/3}}$

2. Michele_Laino

it is the definition of powers with rational exponent

3. Michele_Laino

now, if I apply the rule of power of power, we can write this: $\huge{\left( {\sqrt[3]{{{x^4}}}} \right)^5} = {\left( {{x^{4/3}}} \right)^5} = {x^{5 \cdot \frac{4}{3}}} = {x^{\frac{{20}}{3}}}$

4. Michele_Laino

$\Large {\left( {\sqrt[3]{{{x^4}}}} \right)^5} = {\left( {{x^{4/3}}} \right)^5} = {x^{5 \cdot \frac{4}{3}}} = {x^{\frac{{20}}{3}}}$

5. james1769

okay thnks

6. Michele_Laino

:)