Problem 96 - College Algebra

Question

Simplify using properties of exponents. $$\left(x^{\frac{4}{5}}\right)^{5}$$

Step-by-Step Solution

Answer

The simplified form of the expression \(\left(x^{\frac{4}{5}}\right)^{5}\) is \(x^4\)

Step 1: Identify the Expression

Identify the expression that needs simplification, which in this case is \(\left(x^{\frac{4}{5}}\right)^{5}\)

Step 2: Apply the Property of Exponents

Next, apply the exponent property that states when there is an exponent raised to another exponent, they should be multiplied. Hence, the exponents \(\frac{4}{5}\) and 5 are multiplied.

Step 3: Perform the Multiplication

Multiply the exponents together to simplify the expression: \(\frac{4}{5} * 5\)

Step 4: Simplify the Expression

After performing the multiplication, the resulting expression becomes \(x^4\)