Solve 20ab*3ab^3div5a^2b

$$20 a b \times 3 a b ^ { 3 } \div 5 a ^ { 2 } b$$

Evaluate

$$12a^{4}b^{5}$$

Solution Steps

Multiply a and a to get a^{2}.

$$\frac{20a^{2}b\times 3b^{3}}{5}a^{2}b$$

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

$$\frac{20a^{2}b^{4}\times 3}{5}a^{2}b$$

Multiply 20 and 3 to get 60.

$$\frac{60a^{2}b^{4}}{5}a^{2}b$$

Divide 60a^{2}b^{4} by 5 to get 12a^{2}b^{4}.

$$12a^{2}b^{4}a^{2}b$$

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

$$12a^{4}b^{4}b$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$12a^{4}b^{5}$$

Differentiate w.r.t. a

$$48a^{3}b^{5}$$