Solve 42a^5b^6/-6a^3b=

$$\frac { 42 a ^ { 5 } b ^ { 6 } } { - 6 a ^ { 3 } b } =$$

Evaluate

$$-7a^{2}b^{5}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{42^{1}a^{5}b^{6}}{\left(-6\right)^{1}a^{3}b^{1}}$$

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

$$\frac{42^{1}}{\left(-6\right)^{1}}a^{5-3}b^{6-1}$$

Subtract 3 from 5.

$$\frac{42^{1}}{\left(-6\right)^{1}}a^{2}b^{6-1}$$

Subtract 1 from 6.

$$\frac{42^{1}}{\left(-6\right)^{1}}a^{2}b^{5}$$

Divide 42 by -6.

$$-7a^{2}b^{5}$$

Differentiate w.r.t. b

$$-35a^{2}b^{4}$$