Solve 30a^7b^9/15a^5b^10

$$\frac { 30 a ^ { 7 } b ^ { 9 } } { 15 a ^ { 5 } b ^ { 10 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{30^{1}a^{7}b^{9}}{15^{1}a^{5}b^{10}}$$

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

$$\frac{30^{1}}{15^{1}}a^{7-5}b^{9-10}$$

Subtract 5 from 7.

$$\frac{30^{1}}{15^{1}}a^{2}b^{9-10}$$

Subtract 10 from 9.

$$\frac{30^{1}}{15^{1}}a^{2}\times \frac{1}{b}$$

Divide 30 by 15.

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

Differentiate w.r.t. b

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