Solve frac{5a^{-1}b^{-3}c^5}{2a^-2b^4c^3}

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

Evaluate

$$\frac{5ac^{2}}{2b^{7}}$$

Solution Steps

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

$$\frac{5b^{-3}\times \frac{1}{a}c^{2}}{2a^{-2}b^{4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{5a^{1}c^{2}}{2b^{7}}$$

Calculate a to the power of 1 and get a.

$$\frac{5ac^{2}}{2b^{7}}$$

Differentiate w.r.t. c

$$\frac{5ac}{b^{7}}$$