Solve =(-75a^{5/2}b^{-3/5}r^-9/8)div(-150a^1/2b^-12/5r^-1/8)

$$= ( - 75 a ^ { 5 / 2 } b ^ { - 3 / 5 } r ^ { - 9 / 8 } ) \div ( - 150 a ^ { 1 / 2 } b ^ { - 12 / 5 } r ^ { - 1 / 8 } )$$

Evaluate

$$\frac{b^{\frac{9}{5}}a^{2}}{2r}$$

Solution Steps

Cancel out 75\sqrt{a} in both numerator and denominator.

$$\frac{-r^{-\frac{9}{8}}b^{-\frac{3}{5}}a^{2}}{-2b^{-\frac{12}{5}}r^{-\frac{1}{8}}}$$

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

$$\frac{-r^{-\frac{9}{8}}b^{\frac{9}{5}}a^{2}}{-2r^{-\frac{1}{8}}}$$

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

$$\frac{-b^{\frac{9}{5}}a^{2}}{-2r^{1}}$$

Calculate r to the power of 1 and get r.

$$\frac{-b^{\frac{9}{5}}a^{2}}{-2r}$$

Cancel out -1 in both numerator and denominator.

$$\frac{b^{\frac{9}{5}}a^{2}}{2r}$$

Differentiate w.r.t. b

$$\frac{9b^{\frac{4}{5}}a^{2}}{10r}$$