Q18. - Algebra 1

Question

Simplify each expression.

$\frac{1}{2}{\left(\mathbf{2}{x}^3\right)}^3$

Step-by-Step Solution

Answer

The expression $\frac{1}{2}{\left(2x^3\right)}^3$ can be simplified as $\mathbf{4}{x}^9$.

Step 1. Write the property of power of a power.

For any real number a and any integers m and n, ${\left(a^m\right)}^n=a^{m\cdot n}$.

Step 2. Apply the property of power of a power.

Apply the property of power of a power to the expression in step 1.

$\frac{1}{2}\cdot 2^{1\cdot 3}{x}^{3\cdot 3}=2^2{x}^9$

Step 3. Simplify obtained expression.

Simplify the obtained expression in step 2.

$4x^9$

Therefore, $\frac{1}{2}{\left(2x^3\right)}^3$ can be simplified to width="26" height="22" style="max-width: none; vertical-align: -4px;" $4x^9$.