Question

Simplify each expression.

${\left(\mathbf{6}{x}^3{y}^2\right)}^2$

Short answer

The expression ${\left(6x^3{y}^2\right)}^2$can be simplified as width="53">36x6y4.

Step-by-step solution

Step 1. Write property of power of a product.

For any real number x, y and any integer n, ${\left(xy\right)}^n=x^n{y}^n$.

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

Apply the property of power of a product to the given expression.

$6^2{\left(x^3\right)}^2{\left(y^2\right)}^2$

Step 3. 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 4. Apply the property of power of a power.

Apply the property of power of a power to the expression in step 2.

$6^{2\cdot 1}{x}^{3\cdot 2}{y}^{2\cdot 2}$

Step 5. Simplify the obtained expression.

Simplify the expression in step.

$36x^6{y}^4$

Therefore,${\left(6x^3{y}^2\right)}^2$ can be simplified to $36x^6{y}^4$.