Solve (12u^-2y^2z^-1)^3

$$( 12 u ^ { - 2 } y ^ { 2 } z ^ { - 1 } ) ^ { 3 }$$

Evaluate

$$\frac{1728\times \left(\frac{y}{u}\right)^{6}}{z^{3}}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(12u^{-2}y^{2}\times \frac{1}{z}\right)^{3}$$

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

$$12^{3}\left(u^{-2}\right)^{3}\left(y^{2}\right)^{3}\times \left(\frac{1}{z}\right)^{3}$$

Raise 12 to the power 3.

$$1728\left(u^{-2}\right)^{3}\left(y^{2}\right)^{3}\times \left(\frac{1}{z}\right)^{3}$$

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

$$1728u^{-2\times 3}y^{2\times 3}z^{-3}$$

Multiply -2 times 3.

$$1728\times \frac{1}{u^{6}}y^{2\times 3}z^{-3}$$

Multiply 2 times 3.

$$1728\times \frac{1}{u^{6}}y^{6}z^{-3}$$

Multiply -1 times 3.

$$1728\times \frac{1}{u^{6}}y^{6}\times \frac{1}{z^{3}}$$

Expand

$$\frac{1728\times \left(\frac{y}{u}\right)^{6}}{z^{3}}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(12u^{-2}y^{2}\times \frac{1}{z}\right)^{3}$$

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

$$12^{3}\left(u^{-2}\right)^{3}\left(y^{2}\right)^{3}\times \left(\frac{1}{z}\right)^{3}$$

Raise 12 to the power 3.

$$1728\left(u^{-2}\right)^{3}\left(y^{2}\right)^{3}\times \left(\frac{1}{z}\right)^{3}$$

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

$$1728u^{-2\times 3}y^{2\times 3}z^{-3}$$

Multiply -2 times 3.

$$1728\times \frac{1}{u^{6}}y^{2\times 3}z^{-3}$$

Multiply 2 times 3.

$$1728\times \frac{1}{u^{6}}y^{6}z^{-3}$$

Multiply -1 times 3.

$$1728\times \frac{1}{u^{6}}y^{6}\times \frac{1}{z^{3}}$$