Solve 9a^3b^5/-3ab^2

$$\frac { 9 a ^ { 3 } b ^ { 5 } } { - 3 a b ^ { 2 } }$$

Evaluate

$$-3a^{2}b^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{9^{1}a^{3}b^{5}}{\left(-3\right)^{1}a^{1}b^{2}}$$

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

$$\frac{9^{1}}{\left(-3\right)^{1}}a^{3-1}b^{5-2}$$

Subtract 1 from 3.

$$\frac{9^{1}}{\left(-3\right)^{1}}a^{2}b^{5-2}$$

Subtract 2 from 5.

$$\frac{9^{1}}{\left(-3\right)^{1}}a^{2}b^{3}$$

Divide 9 by -3.

$$-3a^{2}b^{3}$$

Differentiate w.r.t. b

$$-9\left(ab\right)^{2}$$