Solve (x^6y^-6/z^-5)^-5

$$( \frac { x ^ { 6 } y ^ { - 6 } } { z ^ { - 5 } } ) ^ { - 5 }$$

Evaluate

$$\frac{\left(\frac{y}{x}\right)^{30}}{z^{25}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{x^{6}y^{-6}}{z^{-5}}\right)^{-5}$$

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

$$\frac{\left(x^{6}\right)^{-5}\left(y^{-6}\right)^{-5}}{\left(z^{-5}\right)^{-5}}$$

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

$$\frac{x^{6\left(-5\right)}y^{-6\left(-5\right)}}{z^{-5\left(-5\right)}}$$

Multiply 6 times -5.

$$\frac{x^{-30}y^{-6\left(-5\right)}}{z^{-5\left(-5\right)}}$$

Multiply -6 times -5.

$$\frac{x^{-30}y^{30}}{z^{-5\left(-5\right)}}$$

Multiply -5 times -5.

$$\frac{x^{-30}y^{30}}{z^{25}}$$

Expand

$$\frac{\left(\frac{y}{x}\right)^{30}}{z^{25}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{x^{6}y^{-6}}{z^{-5}}\right)^{-5}$$

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

$$\frac{\left(x^{6}\right)^{-5}\left(y^{-6}\right)^{-5}}{\left(z^{-5}\right)^{-5}}$$

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

$$\frac{x^{6\left(-5\right)}y^{-6\left(-5\right)}}{z^{-5\left(-5\right)}}$$

Multiply 6 times -5.

$$\frac{x^{-30}y^{-6\left(-5\right)}}{z^{-5\left(-5\right)}}$$

Multiply -6 times -5.

$$\frac{x^{-30}y^{30}}{z^{-5\left(-5\right)}}$$

Multiply -5 times -5.

$$\frac{x^{-30}y^{30}}{z^{25}}$$