Solve 3a^5b^-7/a^3b^-6

$$\frac { 3 a ^ { 5 } b ^ { - 7 } } { a ^ { 3 } b ^ { - 6 } }$$

Evaluate

$$\frac{3a^{2}}{b}$$

Solution Steps

Cancel out a^{3} in both numerator and denominator.

$$\frac{3b^{-7}a^{2}}{b^{-6}}$$

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

$$\frac{3a^{2}}{b^{1}}$$

Calculate b to the power of 1 and get b.

$$\frac{3a^{2}}{b}$$

Differentiate w.r.t. b

$$-3\times \left(\frac{a}{b}\right)^{2}$$