Solve frac{(r^{2}s^{-1})^0(r^-3s)^2}{(4s)^-3}

$$\frac { ( r ^ { 2 } s ^ { - 1 } ) ^ { 0 } ( r ^ { - 3 } s ) ^ { 2 } } { ( 4 s ) ^ { - 3 } }$$

Evaluate

$$\frac{64s^{5}}{r^{6}}$$

Solution Steps

Calculate r^{2}s^{-1} to the power of 0 and get 1.

$$\frac{1\left(r^{-3}s\right)^{2}}{\left(4s\right)^{-3}}$$

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

$$\frac{1\left(r^{-3}\right)^{2}s^{2}}{\left(4s\right)^{-3}}$$

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

$$\frac{1r^{-6}s^{2}}{\left(4s\right)^{-3}}$$

Expand \left(4s\right)^{-3}.

$$\frac{1r^{-6}s^{2}}{4^{-3}s^{-3}}$$

Calculate 4 to the power of -3 and get \frac{1}{64}.

$$\frac{1r^{-6}s^{2}}{\frac{1}{64}s^{-3}}$$

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

$$\frac{r^{-6}s^{5}}{\frac{1}{64}}$$

Divide r^{-6}s^{5} by \frac{1}{64} by multiplying r^{-6}s^{5} by the reciprocal of \frac{1}{64}.

$$r^{-6}s^{5}\times 64$$

Differentiate w.r.t. r

$$-\frac{384s^{5}}{r^{7}}$$