Solve 6a^4b^6div(-3a^2b^3)

$$6 a ^ { 4 } b ^ { 6 } \div ( - 3 a ^ { 2 } b ^ { 3 } )$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 2 from 4.

$$\frac{6^{1}}{\left(-3\right)^{1}}a^{2}b^{6-3}$$

Subtract 3 from 6.

$$\frac{6^{1}}{\left(-3\right)^{1}}a^{2}b^{3}$$

Divide 6 by -3.

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

Differentiate w.r.t. b

$$-6\left(ab\right)^{2}$$