Problem 39 - College Algebra Essentials

Question

Simplify each exponential expression. $$\left(8 x^{3}\right)^{2}$$

Step-by-Step Solution

Answer

The simplified form of the expression \( (8x^{3})^{2} \) is \( 64x^{6} \)

Step 1: Distribute the Exponent

First off, distribute the outside exponent to both the number and the variable inside the parenthesis. So, the expression is rewritten as \( (8^{2})(x^{3*2}) \).

Step 2: Simplify the Expression

Simplify the expression by performing the exponentiation. The number 8 is squared, and the exponents are multiplied in the variable term. This leads to \( (64)(x^{6}) \)

Step 3: Write the Final Answer

The simplified exponential expression is obtained by multiplying the number and the variable term, which is \( 64x^{6} \) .