Solve 14a^3b^5/49a^4b

$$\frac { 14 a ^ { 3 } b ^ { 5 } } { 49 a ^ { 4 } b }$$

Evaluate

$$\frac{2b^{4}}{7a}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{14^{1}a^{3}b^{5}}{49^{1}a^{4}b^{1}}$$

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

$$\frac{14^{1}}{49^{1}}a^{3-4}b^{5-1}$$

Subtract 4 from 3.

$$\frac{14^{1}}{49^{1}}\times \frac{1}{a}b^{5-1}$$

Subtract 1 from 5.

$$\frac{14^{1}}{49^{1}}\times \frac{1}{a}b^{4}$$

Reduce the fraction \frac{14}{49} to lowest terms by extracting and canceling out 7.

$$\frac{2}{7}\times \frac{1}{a}b^{4}$$

Differentiate w.r.t. b

$$\frac{8b^{3}}{7a}$$