Solve (u^-1y^2z^-3)^3

$$( u ^ { - 1 } y ^ { 2 } z ^ { - 3 } ) ^ { 3 }$$

Evaluate

$$\frac{y^{6}}{u^{3}z^{9}}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

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

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

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

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

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

Multiply -1 times 3.

$$\frac{1}{u^{3}}y^{2\times 3}z^{-3\times 3}$$

Multiply 2 times 3.

$$\frac{1}{u^{3}}y^{6}z^{-3\times 3}$$

Multiply -3 times 3.

$$\frac{1}{u^{3}}y^{6}\times \frac{1}{z^{9}}$$

Expand

$$\frac{y^{6}}{u^{3}z^{9}}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

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

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

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

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

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

Multiply -1 times 3.

$$\frac{1}{u^{3}}y^{2\times 3}z^{-3\times 3}$$

Multiply 2 times 3.

$$\frac{1}{u^{3}}y^{6}z^{-3\times 3}$$

Multiply -3 times 3.

$$\frac{1}{u^{3}}y^{6}\times \frac{1}{z^{9}}$$