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

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

Evaluate

$$\frac{y^{4}x^{6}}{9}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power -2.

$$\frac{1}{9}\left(x^{-3}\right)^{-2}\left(y^{-2}\right)^{-2}$$

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

$$\frac{1}{9}x^{-3\left(-2\right)}y^{-2\left(-2\right)}$$

Multiply -3 times -2.

$$\frac{1}{9}x^{6}y^{-2\left(-2\right)}$$

Multiply -2 times -2.

$$\frac{1}{9}x^{6}y^{4}$$

Expand

$$\frac{y^{4}x^{6}}{9}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power -2.

$$\frac{1}{9}\left(x^{-3}\right)^{-2}\left(y^{-2}\right)^{-2}$$

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

$$\frac{1}{9}x^{-3\left(-2\right)}y^{-2\left(-2\right)}$$

Multiply -3 times -2.

$$\frac{1}{9}x^{6}y^{-2\left(-2\right)}$$

Multiply -2 times -2.

$$\frac{1}{9}x^{6}y^{4}$$