Problem 69 - College Algebra

Question

Simplify the radical expressions if possible. $$\sqrt[3]{x^{4}}$$

Step-by-Step Solution

Answer

\( x * \sqrt[3]{x} \)

Step 1: Breaking Down the Expression

We break down the expression \( \sqrt[3]{x^{4}} \) into \( \sqrt[3]{x^{3}} \) and \( \sqrt[3]{x} \), because the rule of exponents states that when multiplying two bases with the same exponent, you can add the exponents. In other words, \( x^{3} * x = x^{4} \).

Step 2: Simplifying the cube root of \( x^{3} \)

To simplify the \( \sqrt[3]{x^{3}} \), we find the cube root of \( x^{3} \), which is \( x \). This leaves us with the equation \( x * \sqrt[3]{x} \).

Step 3: Final Expression

After simplifying, we get the simplified radical expression, \( x * \sqrt[3]{x} \), which is the final answer.