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

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

Evaluate

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

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power -2.

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

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

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

Multiply 2 times -2.

$$\frac{1}{9}\times \frac{1}{y^{4}}z^{-3\left(-2\right)}$$

Multiply -3 times -2.

$$\frac{1}{9}\times \frac{1}{y^{4}}z^{6}$$

Expand

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

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power -2.

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

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

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

Multiply 2 times -2.

$$\frac{1}{9}\times \frac{1}{y^{4}}z^{-3\left(-2\right)}$$

Multiply -3 times -2.

$$\frac{1}{9}\times \frac{1}{y^{4}}z^{6}$$