Question

Simplify each expression.

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

Short answer

The expression${\left(2x^2\right)}^3{\left(x^3\right)}^3$ can be simplified as $\mathbf{8}{x}^{15}$.

Step-by-step solution

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.

$2^{1\cdot 3}{x}^{2\cdot 3}{x}^{3\cdot 3}=2^3{x}^6{x}^9$

Step 3. Write the property of product of powers.

For any real number a and any integers m and n, $a^m\cdot a^n=a^{m+n}$.

Step 4. Apply property of product of powers.

Apply the property of product of powers to the expression obtained in step 2.

$8x^{6+9}=8x^{15}$

Therefore,${\left(2x^2\right)}^3{\left(x^3\right)}^3$ can be simplified as $8x^{15}$.