Solve (5rs^-2)^6/(5r^3s)^2

$$\frac { ( 5 r s ^ { - 2 } ) ^ { 6 } } { ( 5 r ^ { 3 } s ) ^ { 2 } }$$

Evaluate

$$\frac{625}{s^{14}}$$

Solution Steps

Expand \left(5rs^{-2}\right)^{6}.

$$\frac{5^{6}r^{6}\left(s^{-2}\right)^{6}}{\left(5r^{3}s\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 6 to get -12.

$$\frac{5^{6}r^{6}s^{-12}}{\left(5r^{3}s\right)^{2}}$$

Calculate 5 to the power of 6 and get 15625.

$$\frac{15625r^{6}s^{-12}}{\left(5r^{3}s\right)^{2}}$$

Expand \left(5r^{3}s\right)^{2}.

$$\frac{15625r^{6}s^{-12}}{5^{2}\left(r^{3}\right)^{2}s^{2}}$$

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

$$\frac{15625r^{6}s^{-12}}{5^{2}r^{6}s^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{15625r^{6}s^{-12}}{25r^{6}s^{2}}$$

Cancel out 25r^{6} in both numerator and denominator.

$$\frac{625s^{-12}}{s^{2}}$$

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

$$\frac{625}{s^{14}}$$

Expand

$$\frac{625}{s^{14}}$$

Solution Steps

Expand \left(5rs^{-2}\right)^{6}.

$$\frac{5^{6}r^{6}\left(s^{-2}\right)^{6}}{\left(5r^{3}s\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 6 to get -12.

$$\frac{5^{6}r^{6}s^{-12}}{\left(5r^{3}s\right)^{2}}$$

Calculate 5 to the power of 6 and get 15625.

$$\frac{15625r^{6}s^{-12}}{\left(5r^{3}s\right)^{2}}$$

Expand \left(5r^{3}s\right)^{2}.

$$\frac{15625r^{6}s^{-12}}{5^{2}\left(r^{3}\right)^{2}s^{2}}$$

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

$$\frac{15625r^{6}s^{-12}}{5^{2}r^{6}s^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{15625r^{6}s^{-12}}{25r^{6}s^{2}}$$

Cancel out 25r^{6} in both numerator and denominator.

$$\frac{625s^{-12}}{s^{2}}$$

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

$$\frac{625}{s^{14}}$$