Solve a^3/8*2/a^4diva^3/6

$$\frac { a ^ { 3 } } { 8 } \cdot \frac { 2 } { a ^ { 4 } } \div \frac { a ^ { 3 } } { 6 }$$

Evaluate

$$\frac{3}{2a^{4}}$$

Solution Steps

Multiply \frac{a^{3}}{8} times \frac{2}{a^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{a^{3}\times 2}{8a^{4}}}{\frac{a^{3}}{6}}$$

Cancel out 2a^{3} in both numerator and denominator.

$$\frac{\frac{1}{4a}}{\frac{a^{3}}{6}}$$

Divide \frac{1}{4a} by \frac{a^{3}}{6} by multiplying \frac{1}{4a} by the reciprocal of \frac{a^{3}}{6}.

$$\frac{6}{4aa^{3}}$$

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

$$\frac{6}{4a^{4}}$$

Differentiate w.r.t. a

$$-\frac{6}{a^{5}}$$