Solve (3a^{2}c^3d)(-5cd^3)(-3ac^2d^2)=

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

Evaluate

$$45a^{3}\left(cd\right)^{6}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

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

$$3a^{3}c^{6}d\left(-5\right)d^{3}\left(-3\right)d^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$3a^{3}c^{6}d^{4}\left(-5\right)\left(-3\right)d^{2}$$

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

$$3a^{3}c^{6}d^{6}\left(-5\right)\left(-3\right)$$

Multiply 3 and -5 to get -15.

$$-15a^{3}c^{6}d^{6}\left(-3\right)$$

Multiply -15 and -3 to get 45.

$$45a^{3}c^{6}d^{6}$$

Differentiate w.r.t. a

$$135a^{2}\left(cd\right)^{6}$$