Question

rewrite the following radical with a rational exponent.

\\\sqrt8{x^3}\\

\\\sqrt8{x^3} = \square\\

(simplify your answer. use integers or fractions for any numbers in the expression.)

Explanation:

⚡ Using what you learned: Integer and Rational Exponents

Step 1: Identify the components of the radical expression

The given expression is:

$$ \sqrt[8]{x^3} $$

Here, the index of the radical is \( 8 \) and the exponent of the radicand is \( 3 \).

Step 2: Apply the rational exponent rule

Using the rule for converting radicals to rational exponents:

$$ \sqrt[n]{a^m} = a^{\frac{m}{n}} $$

Substitute \( m = 3 \) and \( n = 8 \):

$$ x^{\frac{3}{8}} $$

Answer:

$$ x^{\frac{3}{8}} $$