Solve (t^-1u^-2v^6)^8

$$( t ^ { - 1 } u ^ { - 2 } v ^ { 6 } ) ^ { 8 }$$

Evaluate

$$\frac{v^{48}}{t^{8}u^{16}}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(\frac{1}{t}u^{-2}v^{6}\right)^{8}$$

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

$$1^{8}\times \left(\frac{1}{t}\right)^{8}\left(u^{-2}\right)^{8}\left(v^{6}\right)^{8}$$

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

$$t^{-8}u^{-2\times 8}v^{6\times 8}$$

Multiply -1 times 8.

$$\frac{1}{t^{8}}u^{-2\times 8}v^{6\times 8}$$

Multiply -2 times 8.

$$\frac{1}{t^{8}}\times \frac{1}{u^{16}}v^{6\times 8}$$

Multiply 6 times 8.

$$\frac{1}{t^{8}}\times \frac{1}{u^{16}}v^{48}$$

Expand

$$\frac{v^{48}}{t^{8}u^{16}}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(\frac{1}{t}u^{-2}v^{6}\right)^{8}$$

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

$$1^{8}\times \left(\frac{1}{t}\right)^{8}\left(u^{-2}\right)^{8}\left(v^{6}\right)^{8}$$

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

$$t^{-8}u^{-2\times 8}v^{6\times 8}$$

Multiply -1 times 8.

$$\frac{1}{t^{8}}u^{-2\times 8}v^{6\times 8}$$

Multiply -2 times 8.

$$\frac{1}{t^{8}}\times \frac{1}{u^{16}}v^{6\times 8}$$

Multiply 6 times 8.

$$\frac{1}{t^{8}}\times \frac{1}{u^{16}}v^{48}$$