Solve (5a^{2}b)(-3a^2b^2c^2)(-2ab^2)

$$( 5 a ^ { 2 } b ) ( - 3 a ^ { 2 } b ^ { 2 } c ^ { 2 } ) ( - 2 a b ^ { 2 } )$$

Evaluate

$$30c^{2}\left(ab\right)^{5}$$

Solution Steps

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

$$5a^{4}b\left(-3\right)b^{2}c^{2}\left(-2\right)ab^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$5a^{5}b\left(-3\right)b^{2}c^{2}\left(-2\right)b^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$5a^{5}b^{3}\left(-3\right)c^{2}\left(-2\right)b^{2}$$

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

$$5a^{5}b^{5}\left(-3\right)c^{2}\left(-2\right)$$

Multiply 5 and -3 to get -15.

$$-15a^{5}b^{5}c^{2}\left(-2\right)$$

Multiply -15 and -2 to get 30.

$$30a^{5}b^{5}c^{2}$$

Differentiate w.r.t. c

$$60c\left(ab\right)^{5}$$