Solve (4)div3/5a^2b^3div3a^2b

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

Evaluate

$$\frac{20\left(ab\right)^{4}}{9}$$

Solution Steps

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

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

Multiply 4 and \frac{5}{3} to get \frac{20}{3}.

$$\frac{\frac{20}{3}a^{2}b^{3}}{3}a^{2}b$$

Divide \frac{20}{3}a^{2}b^{3} by 3 to get \frac{20}{9}a^{2}b^{3}.

$$\frac{20}{9}a^{2}b^{3}a^{2}b$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{20}{9}a^{4}b^{3}b$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{20}{9}a^{4}b^{4}$$

Differentiate w.r.t. a

$$\frac{80a^{3}b^{4}}{9}$$