Question

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.

Answer 1

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

Answer 2

it is the definition of powers with rational exponent

Answer 3

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

Answer 4

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

Answer 5

okay thnks

Answer 6

:)