Question

question 5 (1 point) (03.01 mc) rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents. y^(1/2) * y^(3/4) a) ∛(y^8) b) ∛(y^4) c) ∛(y) d) ∛(y^2)

Explanation:

Step1: Recall exponent - radical conversion rule

The rule is $x^{\frac{m}{n}}=\sqrt[n]{x^{m}}$. Given the expression $y^{\frac{3}{4}}+y^{\frac{1}{2}}$, for $y^{\frac{3}{4}}$, by the rule, it can be written as $\sqrt[4]{y^{3}}$, and for $y^{\frac{1}{2}}$, it can be written as $\sqrt{y}$. But since we are only dealing with the first - term $y^{\frac{3}{4}}$ in the context of the multiple - choice options, $y^{\frac{3}{4}}=\sqrt[4]{y^{3}}$.

Answer:

B. $\sqrt[4]{y^{3}}$