Solve frac{7a^{-1}*c^{-5}*1*b^{3}}{b^2*b^-2*c^-7*a^7}

$$\frac { 7 a ^ { - 1 } \cdot c ^ { - 5 } \cdot 1 \cdot b ^ { 3 } } { b ^ { 2 } \cdot b ^ { - 2 } \cdot c ^ { - 7 } \cdot a ^ { 7 } }$$

Evaluate

$$\frac{7c^{2}b^{3}}{a^{8}}$$

Solution Steps

Multiply b^{2} and b^{-2} to get 1.

$$\frac{7a^{-1}c^{-5}\times 1b^{3}}{c^{-7}a^{7}}$$

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

$$\frac{7\times \frac{1}{a}c^{2}b^{3}}{a^{7}}$$

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

$$\frac{7c^{2}b^{3}}{a^{8}}$$

Differentiate w.r.t. b

$$\frac{21\left(bc\right)^{2}}{a^{8}}$$