Solve (m^6n^3)^2=

$$( m ^ { 6 } n ^ { 3 } ) ^ { 2 } =$$

Evaluate

$$n^{6}m^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(m^{6}n^{3}\right)^{2}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(m^{6}\right)^{2}\left(n^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents.

$$m^{6\times 2}n^{3\times 2}$$

Multiply 6 times 2.

$$m^{12}n^{3\times 2}$$

Multiply 3 times 2.

$$m^{12}n^{6}$$

Expand

$$n^{6}m^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(m^{6}n^{3}\right)^{2}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(m^{6}\right)^{2}\left(n^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents.

$$m^{6\times 2}n^{3\times 2}$$

Multiply 6 times 2.

$$m^{12}n^{3\times 2}$$

Multiply 3 times 2.

$$m^{12}n^{6}$$