Solve 3/5a^2b^2div4/15a

$$\frac { 3 } { 5 } a ^ { 2 } b ^ { 2 } \div \frac { 4 } { 15 } a$$

Evaluate

$$\frac{9b^{2}a^{3}}{4}$$

Solution Steps

Divide \frac{3}{5}a^{2}b^{2} by \frac{4}{15} by multiplying \frac{3}{5}a^{2}b^{2} by the reciprocal of \frac{4}{15}.

$$\frac{\frac{3}{5}a^{2}b^{2}\times 15}{4}a$$

Multiply \frac{3}{5} and 15 to get 9.

$$\frac{9a^{2}b^{2}}{4}a$$

Express \frac{9a^{2}b^{2}}{4}a as a single fraction.

$$\frac{9a^{2}b^{2}a}{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{9a^{3}b^{2}}{4}$$

Differentiate w.r.t. b

$$\frac{9ba^{3}}{2}$$