Question

(Multiple Choice, 20 Points)

Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents:

three to the one third power all over three to the one sixth power

A. the square root of three to the one sixth power
B. the ninth root of three squared
C. the square root of three to the sixth power
D. the sixth root of three

Answer 1

D

$\displaystyle \frac{y^{\frac{1}{3}}}{y^{\frac{1}{6}}}$

$\displaystyle y^{\frac{1}{3}-\frac{1}{6}}$

$\displaystyle y^{\frac{1}{6}}$

$\displaystyle \sqrt[6]{y}$

Answer 2

The expression $\frac{3^{\frac{1}{3}}}{3^{\frac{1}{6}}}$  represents $\sqrt[6]{3}$ as rational exponents as a radical expression.

What is an expression?

"An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation in it."

The given expression is:

$\frac{3^{\frac{1}{3}}}{3^{\frac{1}{6}}}$

= $3^{\frac{1}{3}-\frac{1}{6}}$

= $3^{\frac{1}{6} }$

= $\sqrt[6]{3}$

Learn more about an expression here: https://brainly.com/question/13210674

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