Q. 8.54 - Intermediate Algebra

Question

Write with a rational exponent:

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

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

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

Step-by-Step Solution

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 $8{\left(2a\right)}^{\frac{1}{3}}$

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 $8{\left(2a\right)}^{\frac{1}{3}}$