Solve 5a^3/4b^3/5/20a^1/5b^1/4

$$\frac { 5 a ^ { 3 / 4 } b ^ { 3 / 5 } } { 20 a ^ { 1 / 5 } b ^ { 1 / 4 } }$$

Evaluate

$$\frac{b^{\frac{7}{20}}a^{\frac{11}{20}}}{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{5^{1}a^{\frac{3}{4}}b^{\frac{3}{5}}}{20^{1}\sqrt[5]{a}\sqrt[4]{b}}$$

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

$$\frac{5^{1}}{20^{1}}a^{\frac{3}{4}-\frac{1}{5}}b^{\frac{3}{5}-\frac{1}{4}}$$

Subtract \frac{1}{5} from \frac{3}{4} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$\frac{5^{1}}{20^{1}}a^{\frac{11}{20}}b^{\frac{3}{5}-\frac{1}{4}}$$

Subtract \frac{1}{4} from \frac{3}{5} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$\frac{5^{1}}{20^{1}}a^{\frac{11}{20}}b^{\frac{7}{20}}$$

Reduce the fraction \frac{5}{20} to lowest terms by extracting and canceling out 5.

$$\frac{1}{4}a^{\frac{11}{20}}b^{\frac{7}{20}}$$

Differentiate w.r.t. b

$$\frac{7a^{\frac{11}{20}}}{80b^{\frac{13}{20}}}$$