Solve 36a^2b^3div24a^3b^-2

$$36 a ^ { 2 } b ^ { 3 } \div 24 a ^ { 3 } b ^ { - 2 }$$

Evaluate

$$\frac{3ba^{5}}{2}$$

Solution Steps

Divide 36a^{2}b^{3} by 24 to get \frac{3}{2}a^{2}b^{3}.

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

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{3}{2}a^{5}b^{3}b^{-2}$$

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

$$\frac{3}{2}a^{5}b^{1}$$

Calculate b to the power of 1 and get b.

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

Differentiate w.r.t. a

$$\frac{15ba^{4}}{2}$$