Solve 2a^3b(-1/2ab)a^2b

$$2 a ^ { 3 } b ( - \frac { 1 } { 2 } a b ) a ^ { 2 } b$$

Evaluate

$$-b^{3}a^{6}$$

Solution Steps

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

$$2a^{4}b\left(-\frac{1}{2}\right)ba^{2}b$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$2a^{6}b\left(-\frac{1}{2}\right)bb$$

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

$$2a^{6}b^{2}\left(-\frac{1}{2}\right)b$$

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

$$2a^{6}b^{3}\left(-\frac{1}{2}\right)$$

Multiply 2 and -\frac{1}{2} to get -1.

$$-a^{6}b^{3}$$

Differentiate w.r.t. a

$$-6b^{3}a^{5}$$