Solve (3a^6b)(-6ab^6c)(-b^7c^8)

$$( 3 a ^ { 6 } b ) ( - 6 a b ^ { 6 } c ) ( - b ^ { 7 } c ^ { 8 } )$$

Evaluate

$$18a^{7}c^{9}b^{14}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$3a^{7}b\left(-6\right)b^{6}c\left(-b^{7}\right)c^{8}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$3a^{7}b^{7}\left(-6\right)c\left(-b^{7}\right)c^{8}$$

To multiply powers of the same base, add their exponents. Add 1 and 8 to get 9.

$$3a^{7}b^{7}\left(-6\right)c^{9}\left(-b^{7}\right)$$

Multiply 3 and -6 to get -18.

$$-18a^{7}b^{7}c^{9}\left(-b^{7}\right)$$

Multiply -18 and -1 to get 18.

$$18a^{7}b^{7}c^{9}b^{7}$$

To multiply powers of the same base, add their exponents. Add 7 and 7 to get 14.

$$18a^{7}b^{14}c^{9}$$

Differentiate w.r.t. a

$$126a^{6}c^{9}b^{14}$$