Solve (x^-7y^-2/a^-5)^-4

$$( \frac { x ^ { - 7 } y ^ { - 2 } } { a ^ { - 5 } } ) ^ { - 4 }$$

Evaluate

$$\frac{y^{8}x^{28}}{a^{20}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{x^{-7}y^{-2}}{a^{-5}}\right)^{-4}$$

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

$$\frac{\left(x^{-7}\right)^{-4}\left(y^{-2}\right)^{-4}}{\left(a^{-5}\right)^{-4}}$$

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

$$\frac{x^{-7\left(-4\right)}y^{-2\left(-4\right)}}{a^{-5\left(-4\right)}}$$

Multiply -7 times -4.

$$\frac{x^{28}y^{-2\left(-4\right)}}{a^{-5\left(-4\right)}}$$

Multiply -2 times -4.

$$\frac{x^{28}y^{8}}{a^{-5\left(-4\right)}}$$

Multiply -5 times -4.

$$\frac{x^{28}y^{8}}{a^{20}}$$

Expand

$$\frac{y^{8}x^{28}}{a^{20}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{x^{-7}y^{-2}}{a^{-5}}\right)^{-4}$$

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

$$\frac{\left(x^{-7}\right)^{-4}\left(y^{-2}\right)^{-4}}{\left(a^{-5}\right)^{-4}}$$

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

$$\frac{x^{-7\left(-4\right)}y^{-2\left(-4\right)}}{a^{-5\left(-4\right)}}$$

Multiply -7 times -4.

$$\frac{x^{28}y^{-2\left(-4\right)}}{a^{-5\left(-4\right)}}$$

Multiply -2 times -4.

$$\frac{x^{28}y^{8}}{a^{-5\left(-4\right)}}$$

Multiply -5 times -4.

$$\frac{x^{28}y^{8}}{a^{20}}$$