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

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

Evaluate

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

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power 2.

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

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

$$9y^{3\times 2}z^{-2\times 2}$$

Multiply 3 times 2.

$$9y^{6}z^{-2\times 2}$$

Multiply -2 times 2.

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

Expand

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

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power 2.

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

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

$$9y^{3\times 2}z^{-2\times 2}$$

Multiply 3 times 2.

$$9y^{6}z^{-2\times 2}$$

Multiply -2 times 2.

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