Problem 70 - College Algebra

Question

Simplify the radical expressions if possible. $$\sqrt[3]{x^{5}}$$

Step-by-Step Solution

Answer

The simplified form of the expression \(\sqrt[3]{x^{5}}\) is \(x*\sqrt[3]{x^{2}}\).

Step 1: Identify the exponent inside the radical

The exponent of the variable \(x\) inside the radical is 5.

Step 2: Simplify the expression

The cube root \(\sqrt[3]{x^{5}}\) means we are looking for a number that, when cubed (raised to the power 3), equals \(x^{5}\). We can write the 5 as a multiple of 3, which is the cube root, with some leftover. So, we write 5 as 3+2. Then the expression becomes \(\sqrt[3]{x^{3}} * \sqrt[3]{x^{2}}\). This simplifies to \(x*\sqrt[3]{x^{2}}\) since the cube root of \(x^3\) is \(x\).