Solve 7*(-2a^{2}bc^{3})(-a^2c^3)(-3a^2bc^3)=

$$7 \cdot ( - 2 a ^ { 2 } b c ^ { 3 } ) ( - a ^ { 2 } c ^ { 3 } ) ( - 3 a ^ { 2 } b c ^ { 3 } ) =$$

Evaluate

$$-42b^{2}a^{6}c^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$7\left(-2\right)a^{4}bc^{3}\left(-a^{2}\right)c^{3}\left(-3\right)bc^{3}$$

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

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

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$7\left(-2\right)a^{4}b^{2}c^{6}\left(-a^{2}\right)\left(-3\right)c^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$7\left(-2\right)a^{4}b^{2}c^{9}\left(-a^{2}\right)\left(-3\right)$$

Multiply 7 and -2 to get -14.

$$-14a^{4}b^{2}c^{9}\left(-a^{2}\right)\left(-3\right)$$

Multiply -14 and -3 to get 42.

$$42a^{4}b^{2}c^{9}\left(-a^{2}\right)$$

Multiply 42 and -1 to get -42.

$$-42a^{4}b^{2}c^{9}a^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-42a^{6}b^{2}c^{9}$$

Differentiate w.r.t. b

$$-84ba^{6}c^{9}$$