Solve frac{-25a^frac{3{4}}b^6}{5a^frac{1{2}}b^4}

$$\frac { - 25 a ^ { \frac { 3 } { 4 } } b ^ { 6 } } { 5 a ^ { \frac { 1 } { 2 } } b ^ { 4 } }$$

Evaluate

$$-5\sqrt[4]{a}b^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-25\right)^{1}a^{\frac{3}{4}}b^{6}}{5^{1}\sqrt{a}b^{4}}$$

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

$$\frac{\left(-25\right)^{1}}{5^{1}}a^{\frac{3}{4}-\frac{1}{2}}b^{6-4}$$

Subtract \frac{1}{2} from \frac{3}{4} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$\frac{\left(-25\right)^{1}}{5^{1}}\sqrt[4]{a}b^{6-4}$$

Subtract 4 from 6.

$$\frac{\left(-25\right)^{1}}{5^{1}}\sqrt[4]{a}b^{2}$$

Divide -25 by 5.

$$-5\sqrt[4]{a}b^{2}$$

Differentiate w.r.t. b

$$-10\sqrt[4]{a}b$$