Solve -6a^5b^7/4a^4b^2

$$\frac { - 6 a ^ { 5 } b ^ { 7 } } { 4 a ^ { 4 } b ^ { 2 } }$$

Evaluate

$$-\frac{3ab^{5}}{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-6\right)^{1}a^{5}b^{7}}{4^{1}a^{4}b^{2}}$$

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

$$\frac{\left(-6\right)^{1}}{4^{1}}a^{5-4}b^{7-2}$$

Subtract 4 from 5.

$$\frac{\left(-6\right)^{1}}{4^{1}}a^{1}b^{7-2}$$

Subtract 2 from 7.

$$\frac{\left(-6\right)^{1}}{4^{1}}ab^{5}$$

Reduce the fraction \frac{-6}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{3}{2}ab^{5}$$

Differentiate w.r.t. b

$$-\frac{15ab^{4}}{2}$$