Solve -6a^{4}b^{2}div(-1/2a^2b^2)*(-4a^3b^2)

$$- 6 a ^ { 4 } b ^ { 2 } \div ( - \frac { 1 } { 2 } a ^ { 2 } b ^ { 2 } ) \times ( - 4 a ^ { 3 } b ^ { 2 } )$$

Evaluate

$$-48b^{2}a^{5}$$

Solution Steps

Cancel out a^{2}b^{2} in both numerator and denominator.

$$\frac{-6a^{2}}{-\frac{1}{2}}\left(-4\right)a^{3}b^{2}$$

Divide -6a^{2} by -\frac{1}{2} by multiplying -6a^{2} by the reciprocal of -\frac{1}{2}.

$$\frac{-6a^{2}\times 2}{-1}\left(-4\right)a^{3}b^{2}$$

Anything divided by -1 gives its opposite.

$$6a^{2}\times 2\left(-4\right)a^{3}b^{2}$$

Multiply 6 and 2 to get 12.

$$12a^{2}\left(-4\right)a^{3}b^{2}$$

Multiply 12 and -4 to get -48.

$$-48a^{2}a^{3}b^{2}$$

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

$$-48a^{5}b^{2}$$

Differentiate w.r.t. a

$$-240b^{2}a^{4}$$