Question

match the rational exponent expression in column i with the equivalent radical expression in column ii. assume that x is not 0. 6\sqrt3{x} - 6\sqrt3{x} \sqrt3{6x} \frac{1}{\sqrt3{ - 6x}} \frac{-6}{\sqrt3{x}} \frac{1}{\sqrt3{6x}} \sqrt3{ - 6x} \frac{6}{\sqrt3{x}} drag the radical expressions given above to the appropriate box so they match the expression with rational exponents to which they are equivalent. choices may be used once, more than once, or not at all. (a) - 6x^{\frac{1}{3}} (b) - 6x^{-\frac{1}{3}} (c) 6x^{-\frac{1}{3}}

Explanation:

Step1: Recall the rule of rational exponents

The rule is $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$. For $- 6x^{\frac{1}{3}}$, we can rewrite it as $-6\sqrt[3]{x}$. For $-6x^{-\frac{1}{3}}$, using the rule $a^{-n}=\frac{1}{a^{n}}$, we get $\frac{-6}{\sqrt[3]{x}}$. For $6x^{-\frac{1}{3}}$, it becomes $\frac{6}{\sqrt[3]{x}}$. For $6x^{\frac{1}{3}}$, it is $6\sqrt[3]{x}$.

Answer:

(a) $-6\sqrt[3]{x}$
(b) $\frac{-6}{\sqrt[3]{x}}$
(c) $\frac{6}{\sqrt[3]{x}}$