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

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

Evaluate

$$\frac{1}{64\left(uv\right)^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power -3.

$$\frac{1}{64}\left(u^{2}\right)^{-3}\left(v^{2}\right)^{-3}$$

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

$$\frac{1}{64}u^{2\left(-3\right)}v^{2\left(-3\right)}$$

Multiply 2 times -3.

$$\frac{1}{64}\times \frac{1}{u^{6}}v^{2\left(-3\right)}$$

Multiply 2 times -3.

$$\frac{1}{64}\times \frac{1}{u^{6}}\times \frac{1}{v^{6}}$$

Expand

$$\frac{1}{64\left(uv\right)^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power -3.

$$\frac{1}{64}\left(u^{2}\right)^{-3}\left(v^{2}\right)^{-3}$$

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

$$\frac{1}{64}u^{2\left(-3\right)}v^{2\left(-3\right)}$$

Multiply 2 times -3.

$$\frac{1}{64}\times \frac{1}{u^{6}}v^{2\left(-3\right)}$$

Multiply 2 times -3.

$$\frac{1}{64}\times \frac{1}{u^{6}}\times \frac{1}{v^{6}}$$