Solve 15a^2b^6/25a^7b

$$\frac { 15 a ^ { 2 } b ^ { 6 } } { 25 a ^ { 7 } b }$$

Evaluate

$$\frac{3\times \left(\frac{b}{a}\right)^{5}}{5}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{15^{1}a^{2}b^{6}}{25^{1}a^{7}b^{1}}$$

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

$$\frac{15^{1}}{25^{1}}a^{2-7}b^{6-1}$$

Subtract 7 from 2.

$$\frac{15^{1}}{25^{1}}a^{-5}b^{6-1}$$

Subtract 1 from 6.

$$\frac{15^{1}}{25^{1}}\times \frac{1}{a^{5}}b^{5}$$

Reduce the fraction \frac{15}{25} to lowest terms by extracting and canceling out 5.

$$\frac{3}{5}\times \frac{1}{a^{5}}b^{5}$$

Differentiate w.r.t. b

$$\frac{3b^{4}}{a^{5}}$$