Question

describe how to transform (in photo) into an expression with a rational exponent. Make sure you respond with complete sentences

Answer 1

SOLUTION

Write out the expression given

$(\sqrt[5]{x^7)}^3$

The fifth root of a number is 1/5 of the number at the exponent

Hence

$(x^7)^{\frac{1}{5}}=x^{\frac{7}{5}}$

Then, take the cube of the last exponent

$\begin{gathered} (x^{\frac{7}{5}})^3 \\ \end{gathered}$

Using the product power rule we take the product of the exponent

$\begin{gathered} ^{}(x^a)^b=x^{ab} \\ \text{Then } \\ (x^{\frac{7}{5}})^3=x^{\frac{7}{5}\times3}=x^{\frac{21}{5}} \end{gathered}$

Hence

The rational exponent of the given expression is

$x^{\frac{21}{5}}$

The rational exponent of the given expression is x^21/5

Note; 21/5 is the exponent