Solve frac{-4a^{-2}b^{6}}{c^{2}a^{-4}}*8b^6d^-6/a^-15e^9

$$\frac { - 4 a ^ { - 2 } b ^ { 6 } } { c ^ { 2 } a ^ { - 4 } } \cdot \frac { 8 b ^ { 6 } d ^ { - 6 } } { a ^ { - 15 } e ^ { 9 } }$$

Evaluate

$$-\frac{32b^{12}a^{17}}{e^{9}c^{2}d^{6}}$$

Solution Steps

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

$$\frac{-4a^{2}b^{6}}{c^{2}}\times \frac{8b^{6}d^{-6}}{a^{-15}e^{9}}$$

Multiply \frac{-4a^{2}b^{6}}{c^{2}} times \frac{8b^{6}d^{-6}}{a^{-15}e^{9}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-4a^{2}b^{6}\times 8b^{6}d^{-6}}{c^{2}a^{-15}e^{9}}$$

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

$$\frac{-4\times 8d^{-6}b^{6}b^{6}a^{17}}{e^{9}c^{2}}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$\frac{-4\times 8d^{-6}b^{12}a^{17}}{e^{9}c^{2}}$$

Multiply -4 and 8 to get -32.

$$\frac{-32d^{-6}b^{12}a^{17}}{e^{9}c^{2}}$$

Differentiate w.r.t. d

$$\frac{192b^{12}a^{17}}{e^{9}c^{2}d^{7}}$$