Solve (1a^2/2)(-2ab/3)(-5a^3b^3/3)=

$$( \frac { 1 a ^ { 2 } } { 2 } ) ( - \frac { 2 a b } { 3 } ) ( - \frac { 5 a ^ { 3 } b ^ { 3 } } { 3 } ) =$$

Evaluate

$$\frac{5b^{4}a^{6}}{9}$$

Solution Steps

Multiply \frac{1a^{2}}{2} times -\frac{2ab}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-a^{2}\times 2ab}{2\times 3}\left(-\frac{5a^{3}b^{3}}{3}\right)$$

Cancel out 2 in both numerator and denominator.

$$\frac{-aba^{2}}{3}\left(-\frac{5a^{3}b^{3}}{3}\right)$$

Multiply \frac{-aba^{2}}{3} times -\frac{5a^{3}b^{3}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(-1\right)aba^{2}\times 5a^{3}b^{3}}{3\times 3}$$

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

$$\frac{-\left(-1\right)a^{3}b\times 5a^{3}b^{3}}{3\times 3}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{-\left(-1\right)a^{6}b\times 5b^{3}}{3\times 3}$$

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

$$\frac{-\left(-1\right)a^{6}b^{4}\times 5}{3\times 3}$$

Multiply -1 and -1 to get 1.

$$\frac{a^{6}b^{4}\times 5}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$\frac{a^{6}b^{4}\times 5}{9}$$

Differentiate w.r.t. b

$$\frac{20b^{3}a^{6}}{9}$$