Solve 9b^3/5c^7*15bc^2

$$\frac { 9 b ^ { 3 } } { 5 c ^ { 7 } } \times 15 b c ^ { 2 }$$

Evaluate

$$\frac{27b^{4}}{c^{5}}$$

Solution Steps

Express \frac{9b^{3}}{5c^{7}}\times 15 as a single fraction.

$$\frac{9b^{3}\times 15}{5c^{7}}bc^{2}$$

Cancel out 5 in both numerator and denominator.

$$\frac{3\times 9b^{3}}{c^{7}}bc^{2}$$

Express \frac{3\times 9b^{3}}{c^{7}}b as a single fraction.

$$\frac{3\times 9b^{3}b}{c^{7}}c^{2}$$

Express \frac{3\times 9b^{3}b}{c^{7}}c^{2} as a single fraction.

$$\frac{3\times 9b^{3}bc^{2}}{c^{7}}$$

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

$$\frac{3\times 9bb^{3}}{c^{5}}$$

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

$$\frac{3\times 9b^{4}}{c^{5}}$$

Multiply 3 and 9 to get 27.

$$\frac{27b^{4}}{c^{5}}$$

Differentiate w.r.t. b

$$\frac{108b^{3}}{c^{5}}$$