Solve 4/5a^4b^5/-frac{3{10}a^2b^7}=

$$\frac { \frac { 4 } { 5 } a ^ { 4 } b ^ { 5 } } { - \frac { 3 } { 10 } a ^ { 2 } b ^ { 7 } } =$$

Evaluate

$$-\frac{8\times \left(\frac{a}{b}\right)^{2}}{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(\frac{4}{5}\right)^{1}a^{4}b^{5}}{\left(-\frac{3}{10}\right)^{1}a^{2}b^{7}}$$

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

$$\frac{\left(\frac{4}{5}\right)^{1}}{\left(-\frac{3}{10}\right)^{1}}a^{4-2}b^{5-7}$$

Subtract 2 from 4.

$$\frac{\left(\frac{4}{5}\right)^{1}}{\left(-\frac{3}{10}\right)^{1}}a^{2}b^{5-7}$$

Subtract 7 from 5.

$$\frac{\left(\frac{4}{5}\right)^{1}}{\left(-\frac{3}{10}\right)^{1}}a^{2}b^{-2}$$

Divide \frac{4}{5} by -\frac{3}{10} by multiplying \frac{4}{5} by the reciprocal of -\frac{3}{10}.

$$-\frac{8}{3}a^{2}\times \frac{1}{b^{2}}$$

Differentiate w.r.t. b

$$\frac{16a^{2}}{3b^{3}}$$