Solve 42x^{3}y^{2}c^3:7x^2y^2c^3=

$$42 x ^ { 3 } y ^ { 2 } c ^ { 3 } : 7 x ^ { 2 } y ^ { 2 } c ^ { 3 } =$$

Evaluate

$$6y^{4}x^{5}c^{6}$$

Solution Steps

Divide 42x^{3}y^{2}c^{3} by 7 to get 6x^{3}y^{2}c^{3}.

$$6x^{3}y^{2}c^{3}x^{2}y^{2}c^{3}$$

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

$$6x^{5}y^{2}c^{3}y^{2}c^{3}$$

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

$$6x^{5}y^{4}c^{3}c^{3}$$

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

$$6x^{5}y^{4}c^{6}$$

Differentiate w.r.t. x

$$30c^{6}\left(xy\right)^{4}$$