Solve (-4m^6n^2)^2

$$( - 4 m ^ { 6 } n ^ { 2 } ) ^ { 2 }$$

Evaluate

$$16n^{4}m^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-4m^{6}n^{2}\right)^{2}$$

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

$$\left(-4\right)^{2}\left(m^{6}\right)^{2}\left(n^{2}\right)^{2}$$

Raise -4 to the power 2.

$$16\left(m^{6}\right)^{2}\left(n^{2}\right)^{2}$$

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

$$16m^{6\times 2}n^{2\times 2}$$

Multiply 6 times 2.

$$16m^{12}n^{2\times 2}$$

Multiply 2 times 2.

$$16m^{12}n^{4}$$

Expand

$$16n^{4}m^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-4m^{6}n^{2}\right)^{2}$$

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

$$\left(-4\right)^{2}\left(m^{6}\right)^{2}\left(n^{2}\right)^{2}$$

Raise -4 to the power 2.

$$16\left(m^{6}\right)^{2}\left(n^{2}\right)^{2}$$

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

$$16m^{6\times 2}n^{2\times 2}$$

Multiply 6 times 2.

$$16m^{12}n^{2\times 2}$$

Multiply 2 times 2.

$$16m^{12}n^{4}$$