Solve (7a^-35b^-3c)(-4a^-88b^-2)=

$$( 7 a ^ { - 3 } 5 b ^ { - 3 } c ) ( - 4 a ^ { - 8 } 8 b ^ { - 2 } ) =$$

Evaluate

$$-\frac{1120c}{b^{5}a^{11}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and -8 to get -11.

$$7a^{-11}\times 5b^{-3}c\left(-4\right)\times 8b^{-2}$$

To multiply powers of the same base, add their exponents. Add -3 and -2 to get -5.

$$7a^{-11}\times 5b^{-5}c\left(-4\right)\times 8$$

Multiply 7 and 5 to get 35.

$$35a^{-11}b^{-5}c\left(-4\right)\times 8$$

Multiply 35 and -4 to get -140.

$$-140a^{-11}b^{-5}c\times 8$$

Multiply -140 and 8 to get -1120.

$$-1120a^{-11}b^{-5}c$$

Differentiate w.r.t. c

$$-\frac{1120}{b^{5}a^{11}}$$