Solve a^{4}b(-1/2)^3a^2(5/2)b^3(-4)a^2

$$a ^ { 4 } b ( - \frac { 1 } { 2 } ) ^ { 3 } a ^ { 2 } ( \frac { 5 } { 2 } ) b ^ { 3 } ( - 4 ) a ^ { 2 }$$

Evaluate

$$\frac{5b^{4}a^{8}}{4}$$

Solution Steps

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

$$a^{6}b\left(-\frac{1}{2}\right)^{3}\times \frac{5}{2}b^{3}\left(-4\right)a^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$a^{8}b\left(-\frac{1}{2}\right)^{3}\times \frac{5}{2}b^{3}\left(-4\right)$$

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

$$a^{8}b^{4}\left(-\frac{1}{2}\right)^{3}\times \frac{5}{2}\left(-4\right)$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$a^{8}b^{4}\left(-\frac{1}{8}\right)\times \frac{5}{2}\left(-4\right)$$

Multiply -\frac{1}{8} and \frac{5}{2} to get -\frac{5}{16}.

$$a^{8}b^{4}\left(-\frac{5}{16}\right)\left(-4\right)$$

Multiply -\frac{5}{16} and -4 to get \frac{5}{4}.

$$a^{8}b^{4}\times \frac{5}{4}$$

Differentiate w.r.t. b

$$5b^{3}a^{8}$$