Solve 2ab^{2}*4a^2b^-1*3a^-2b^2

$$2 a b ^ { 2 } \times 4 a ^ { 2 } b ^ { - 1 } \times 3 a ^ { - 2 } b ^ { 2 }$$

Evaluate

$$24ab^{3}$$

Solution Steps

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

$$2a^{3}b^{2}\times 4b^{-1}\times 3a^{-2}b^{2}$$

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

$$2a^{1}b^{2}\times 4b^{-1}\times 3b^{2}$$

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

$$2a^{1}b^{1}\times 4\times 3b^{2}$$

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

$$2a^{1}b^{3}\times 4\times 3$$

Calculate a to the power of 1 and get a.

$$2ab^{3}\times 4\times 3$$

Multiply 2 and 4 to get 8.

$$8ab^{3}\times 3$$

Multiply 8 and 3 to get 24.

$$24ab^{3}$$

Differentiate w.r.t. a

$$24b^{3}$$