Solve (t^-6u^-4)^5

$$( t ^ { - 6 } u ^ { - 4 } ) ^ { 5 }$$

Evaluate

$$\frac{1}{u^{20}t^{30}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(t^{-6}u^{-4}\right)^{5}$$

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

$$\left(t^{-6}\right)^{5}\left(u^{-4}\right)^{5}$$

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

$$t^{-6\times 5}u^{-4\times 5}$$

Multiply -6 times 5.

$$\frac{1}{t^{30}}u^{-4\times 5}$$

Multiply -4 times 5.

$$\frac{1}{t^{30}}\times \frac{1}{u^{20}}$$

Expand

$$\frac{1}{u^{20}t^{30}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(t^{-6}u^{-4}\right)^{5}$$

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

$$\left(t^{-6}\right)^{5}\left(u^{-4}\right)^{5}$$

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

$$t^{-6\times 5}u^{-4\times 5}$$

Multiply -6 times 5.

$$\frac{1}{t^{30}}u^{-4\times 5}$$

Multiply -4 times 5.

$$\frac{1}{t^{30}}\times \frac{1}{u^{20}}$$