Problem 95 - College Algebra

Question

Simplify using properties of exponents. $$\left(x^{\frac{2}{3}}\right)^{3}$$

Step-by-Step Solution

Answer

The simplified form of the given expression \(\left(x^{\frac{2}{3}}\right)^{3}\) is \(x^{2}\).

Step 1: Apply the Power of a Power Rule to the expression

In the given expression, \(\left(x^{\frac{2}{3}}\right)^{3}\), the Power of a Power Rule is applied to multiply the exponents. When we multiply the exponents \(\frac{2}{3}\) and 3, the output is 2 as \(\frac{2}{3}\) * 3 equals 2.

Step 2: Simplify to obtain the final expression

After applying the multiplication of exponents, the expression simplifies down to \(x^{2}\). This is the simplified exponent expression.