Solve (5h^{-2}k^0)^3(5k^-2)^-4

$$( 5 h ^ { - 2 } k ^ { 0 } ) ^ { 3 } ( 5 k ^ { - 2 } ) ^ { - 4 }$$

Evaluate

$$\frac{k^{8}}{5h^{6}}$$

Solution Steps

Calculate k to the power of 0 and get 1.

$$\left(5h^{-2}\times 1\right)^{3}\times \left(5k^{-2}\right)^{-4}$$

Multiply 5 and 1 to get 5.

$$\left(5h^{-2}\right)^{3}\times \left(5k^{-2}\right)^{-4}$$

Expand \left(5h^{-2}\right)^{3}.

$$5^{3}\left(h^{-2}\right)^{3}\times \left(5k^{-2}\right)^{-4}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 3 to get -6.

$$5^{3}h^{-6}\times \left(5k^{-2}\right)^{-4}$$

Calculate 5 to the power of 3 and get 125.

$$125h^{-6}\times \left(5k^{-2}\right)^{-4}$$

Expand \left(5k^{-2}\right)^{-4}.

$$125h^{-6}\times 5^{-4}\left(k^{-2}\right)^{-4}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -4 to get 8.

$$125h^{-6}\times 5^{-4}k^{8}$$

Calculate 5 to the power of -4 and get \frac{1}{625}.

$$125h^{-6}\times \frac{1}{625}k^{8}$$

Multiply 125 and \frac{1}{625} to get \frac{1}{5}.

$$\frac{1}{5}h^{-6}k^{8}$$

Expand

$$\frac{k^{8}}{5h^{6}}$$

Solution Steps

Calculate k to the power of 0 and get 1.

$$\left(5h^{-2}\times 1\right)^{3}\times \left(5k^{-2}\right)^{-4}$$

Multiply 5 and 1 to get 5.

$$\left(5h^{-2}\right)^{3}\times \left(5k^{-2}\right)^{-4}$$

Expand \left(5h^{-2}\right)^{3}.

$$5^{3}\left(h^{-2}\right)^{3}\times \left(5k^{-2}\right)^{-4}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 3 to get -6.

$$5^{3}h^{-6}\times \left(5k^{-2}\right)^{-4}$$

Calculate 5 to the power of 3 and get 125.

$$125h^{-6}\times \left(5k^{-2}\right)^{-4}$$

Expand \left(5k^{-2}\right)^{-4}.

$$125h^{-6}\times 5^{-4}\left(k^{-2}\right)^{-4}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -4 to get 8.

$$125h^{-6}\times 5^{-4}k^{8}$$

Calculate 5 to the power of -4 and get \frac{1}{625}.

$$125h^{-6}\times \frac{1}{625}k^{8}$$

Multiply 125 and \frac{1}{625} to get \frac{1}{5}.

$$\frac{1}{5}h^{-6}k^{8}$$