Solve (-2u^3v^4)^4

$$( - 2 u ^ { 3 } v ^ { 4 } ) ^ { 4 }$$

Evaluate

$$16u^{12}v^{16}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-2u^{3}v^{4}\right)^{4}$$

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

$$\left(-2\right)^{4}\left(u^{3}\right)^{4}\left(v^{4}\right)^{4}$$

Raise -2 to the power 4.

$$16\left(u^{3}\right)^{4}\left(v^{4}\right)^{4}$$

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

$$16u^{3\times 4}v^{4\times 4}$$

Multiply 3 times 4.

$$16u^{12}v^{4\times 4}$$

Multiply 4 times 4.

$$16u^{12}v^{16}$$

Expand

$$16u^{12}v^{16}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-2u^{3}v^{4}\right)^{4}$$

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

$$\left(-2\right)^{4}\left(u^{3}\right)^{4}\left(v^{4}\right)^{4}$$

Raise -2 to the power 4.

$$16\left(u^{3}\right)^{4}\left(v^{4}\right)^{4}$$

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

$$16u^{3\times 4}v^{4\times 4}$$

Multiply 3 times 4.

$$16u^{12}v^{4\times 4}$$

Multiply 4 times 4.

$$16u^{12}v^{16}$$