Question

Describe how to transform the expression in the photo into an expression with a rational exponent. Please use complete sentences

Answer 1

$(\sqrt[6]{x^5})^7$

Step 1:

Use the definition of a radical:

$\sqrt[b]{x^a}=x^{\frac{a}{b}}$$\sqrt[6]{x^5}=x^{\frac{5}{6}}$

Step 2:

Use the following property of exponents:

$(x^y)^z=x^{y\cdot z}$

so:

$(x^{\frac{5}{6}})^7=x^{\frac{5}{6}\cdot7}=x^{\frac{35}{6}}$