Solve (3x^-2y^-2)^3

$$( 3 x ^ { - 2 } y ^ { - 2 } ) ^ { 3 }$$

Evaluate

$$\frac{27}{\left(xy\right)^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power 3.

$$27\left(x^{-2}\right)^{3}\left(y^{-2}\right)^{3}$$

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

$$27x^{-2\times 3}y^{-2\times 3}$$

Multiply -2 times 3.

$$27\times \frac{1}{x^{6}}y^{-2\times 3}$$

Multiply -2 times 3.

$$27\times \frac{1}{x^{6}}\times \frac{1}{y^{6}}$$

Expand

$$\frac{27}{\left(xy\right)^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power 3.

$$27\left(x^{-2}\right)^{3}\left(y^{-2}\right)^{3}$$

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

$$27x^{-2\times 3}y^{-2\times 3}$$

Multiply -2 times 3.

$$27\times \frac{1}{x^{6}}y^{-2\times 3}$$

Multiply -2 times 3.

$$27\times \frac{1}{x^{6}}\times \frac{1}{y^{6}}$$