Solve -4x^4y^5z^3div3/9xy^2z=

$$-4 { x }^{ 4 } { y }^{ 5 } { z }^{ 3 } \div \frac{ 3 }{ 9 } x { y }^{ 2 } z=$$

Evaluate

$$-12z^{4}x^{5}y^{7}$$

Solution Steps

Divide -4x^{4}y^{5}z^{3} by \frac{3}{9} by multiplying -4x^{4}y^{5}z^{3} by the reciprocal of \frac{3}{9}.

$$\frac{-4x^{4}y^{5}z^{3}\times 9}{3}xy^{2}z$$

Multiply -4 and 9 to get -36.

$$\frac{-36x^{4}y^{5}z^{3}}{3}xy^{2}z$$

Divide -36x^{4}y^{5}z^{3} by 3 to get -12x^{4}y^{5}z^{3}.

$$-12x^{4}y^{5}z^{3}xy^{2}z$$

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

$$-12x^{5}y^{5}z^{3}y^{2}z$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$-12x^{5}y^{7}z^{3}z$$

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

$$-12x^{5}y^{7}z^{4}$$

Differentiate w.r.t. x

$$-60y^{7}\left(xz\right)^{4}$$