Solve frac{3a^{2}}{5b^{3}}*3c^2/8a^2div9c^5/40b^8=

$$\frac { 3 a ^ { 2 } } { 5 b ^ { 3 } } \cdot \frac { 3 c ^ { 2 } } { 8 a ^ { 2 } } \div \frac { 9 c ^ { 5 } } { 40 b ^ { 8 } } =$$

Evaluate

$$\frac{b^{5}}{c^{3}}$$

Solution Steps

Multiply \frac{3a^{2}}{5b^{3}} times \frac{3c^{2}}{8a^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3a^{2}\times 3c^{2}}{5b^{3}\times 8a^{2}}}{\frac{9c^{5}}{40b^{8}}}$$

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

$$\frac{\frac{3\times 3c^{2}}{5\times 8b^{3}}}{\frac{9c^{5}}{40b^{8}}}$$

Divide \frac{3\times 3c^{2}}{5\times 8b^{3}} by \frac{9c^{5}}{40b^{8}} by multiplying \frac{3\times 3c^{2}}{5\times 8b^{3}} by the reciprocal of \frac{9c^{5}}{40b^{8}}.

$$\frac{3\times 3c^{2}\times 40b^{8}}{5\times 8b^{3}\times 9c^{5}}$$

Cancel out 3\times 3\times 5\times 8c^{2}b^{3} in both numerator and denominator.

$$\frac{b^{5}}{c^{3}}$$

Differentiate w.r.t. c

$$-\frac{3b^{5}}{c^{4}}$$