Solve (5k)^4m^-4/(km)^-3

$$\frac { ( 5 k ) ^ { 4 } m ^ { - 4 } } { ( k m ) ^ { - 3 } }$$

Evaluate

$$\frac{625k^{7}}{m}$$

Solution Steps

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

$$\frac{5^{4}k^{4}m^{-4}}{\left(km\right)^{-3}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{625k^{4}m^{-4}}{\left(km\right)^{-3}}$$

Expand \left(km\right)^{-3}.

$$\frac{625k^{4}m^{-4}}{k^{-3}m^{-3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{625m^{-4}k^{7}}{m^{-3}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{625k^{7}}{m^{1}}$$

Calculate m to the power of 1 and get m.

$$\frac{625k^{7}}{m}$$

Expand

$$\frac{625k^{7}}{m}$$

Solution Steps

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

$$\frac{5^{4}k^{4}m^{-4}}{\left(km\right)^{-3}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{625k^{4}m^{-4}}{\left(km\right)^{-3}}$$

Expand \left(km\right)^{-3}.

$$\frac{625k^{4}m^{-4}}{k^{-3}m^{-3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{625m^{-4}k^{7}}{m^{-3}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{625k^{7}}{m^{1}}$$

Calculate m to the power of 1 and get m.

$$\frac{625k^{7}}{m}$$