Solve (5h^-2k^2)^-3

$$( 5 h ^ { - 2 } k ^ { 2 } ) ^ { - 3 }$$

Evaluate

$$\frac{\left(\frac{h}{k}\right)^{6}}{125}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(5h^{-2}k^{2}\right)^{-3}$$

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

$$5^{-3}\left(h^{-2}\right)^{-3}\left(k^{2}\right)^{-3}$$

Raise 5 to the power -3.

$$\frac{1}{125}\left(h^{-2}\right)^{-3}\left(k^{2}\right)^{-3}$$

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

$$\frac{1}{125}h^{-2\left(-3\right)}k^{2\left(-3\right)}$$

Multiply -2 times -3.

$$\frac{1}{125}h^{6}k^{2\left(-3\right)}$$

Multiply 2 times -3.

$$\frac{1}{125}h^{6}\times \frac{1}{k^{6}}$$

Expand

$$\frac{\left(\frac{h}{k}\right)^{6}}{125}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(5h^{-2}k^{2}\right)^{-3}$$

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

$$5^{-3}\left(h^{-2}\right)^{-3}\left(k^{2}\right)^{-3}$$

Raise 5 to the power -3.

$$\frac{1}{125}\left(h^{-2}\right)^{-3}\left(k^{2}\right)^{-3}$$

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

$$\frac{1}{125}h^{-2\left(-3\right)}k^{2\left(-3\right)}$$

Multiply -2 times -3.

$$\frac{1}{125}h^{6}k^{2\left(-3\right)}$$

Multiply 2 times -3.

$$\frac{1}{125}h^{6}\times \frac{1}{k^{6}}$$