Question

describe how to transform (^5 square root x^7)^3 into an expression with a rational exponent. make sure you respond with complete sentences

Answer 1

Answer:

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

Step-by-step explanation:

We are given an expression and we have to transform it into an expression with exponent.

5th root of x can be written as $x^\frac{1}{5}$

$(\sqrt[5]{x^7})^3\\\\((x^7)^\frac{1}{5} )^3$

The powers outside will be multiplied as: $(x^a)^b = x^{ab}$

$(x^\frac{7}{5} )^3\\x^\frac{7*3}{5}\\x^\frac{21}{5}$

where the exponent is $\frac{21}{5}$ and it is a rational number by definition of rational numbers