Question

Write with a rational exponent:

(a) $\sqrt[7]{3k}$

(b) $\sqrt[4]{5j}$

(c) $8\sqrt[3]{2a}$

Short answer

The rational exponent of $\sqrt[7]{3k}$is${\left(3k\right)}^{\frac{1}{7}}$

The rational exponent of $\sqrt[4]{5j}$is${\left(5j\right)}^{\frac{1}{4}}$

The rational exponent of $8\sqrt[3]{2a}$is$8{\left(2a\right)}^{\frac{1}{3}}$

Step-by-step solution

Part (a) Given

The radical expression $\sqrt[7]{3k}$

To write each radical in the form of$a^{\frac{1}{n}}$

Part (a) Step 2. Write as rational exponent

The index is $7$, so the denominator of the exponent will be $7$.

Put parentheses around the entire expression.

The rational exponent is${\left(3k\right)}^{\frac{1}{7}}$

Part (b) Step 1. Given

The radical expression is$\sqrt[4]{5j}$

To write each radical in the form of$a^{\frac{1}{n}}$

Part (b) Step 2. Write as rational exponent

The index is $4$, so the denominator of the exponent will be $4$

Put parentheses around the entire expression.

The rational exponent is${\left(5j\right)}^{\frac{1}{4}}$

Part (c) Step 1. Given

The radical expression is$8\sqrt[3]{2a}$

To write each radical in the form of$a^{\frac{1}{n}}$

Part (c) Step 2. Write as rational exponent

The index is $3$, so the denominator of the exponent will be $3$

Put parentheses around the entire expression.

The rational exponent is$8{\left(2a\right)}^{\frac{1}{3}}$