Solve (x^4y^-1/z^-8)^-5

$$( \frac { x ^ { 4 } y ^ { - 1 } } { z ^ { - 8 } } ) ^ { - 5 }$$

Evaluate

$$\frac{y^{5}}{x^{20}z^{40}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{x^{4}\times \frac{1}{y}}{z^{-8}}\right)^{-5}$$

To raise the quotient of two numbers to a power, raise each number to the power and then divide.

$$\frac{\left(x^{4}\right)^{-5}\times \left(\frac{1}{y}\right)^{-5}}{\left(z^{-8}\right)^{-5}}$$

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

$$\frac{x^{4\left(-5\right)}y^{-\left(-5\right)}}{z^{-8\left(-5\right)}}$$

Multiply 4 times -5.

$$\frac{x^{-20}y^{-\left(-5\right)}}{z^{-8\left(-5\right)}}$$

Multiply -1 times -5.

$$\frac{x^{-20}y^{5}}{z^{-8\left(-5\right)}}$$

Multiply -8 times -5.

$$\frac{x^{-20}y^{5}}{z^{40}}$$

Expand

$$\frac{y^{5}}{x^{20}z^{40}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{x^{4}\times \frac{1}{y}}{z^{-8}}\right)^{-5}$$

To raise the quotient of two numbers to a power, raise each number to the power and then divide.

$$\frac{\left(x^{4}\right)^{-5}\times \left(\frac{1}{y}\right)^{-5}}{\left(z^{-8}\right)^{-5}}$$

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

$$\frac{x^{4\left(-5\right)}y^{-\left(-5\right)}}{z^{-8\left(-5\right)}}$$

Multiply 4 times -5.

$$\frac{x^{-20}y^{-\left(-5\right)}}{z^{-8\left(-5\right)}}$$

Multiply -1 times -5.

$$\frac{x^{-20}y^{5}}{z^{-8\left(-5\right)}}$$

Multiply -8 times -5.

$$\frac{x^{-20}y^{5}}{z^{40}}$$