Solve 1/3xy^4z^2div1/2xy^2=

$$\frac { 1 } { 3 } x y ^ { 4 } z ^ { 2 } \div \frac { 1 } { 2 } x y ^ { 2 } =$$

Evaluate

$$\frac{2y^{6}\left(xz\right)^{2}}{3}$$

Solution Steps

Divide \frac{1}{3}xy^{4}z^{2} by \frac{1}{2} by multiplying \frac{1}{3}xy^{4}z^{2} by the reciprocal of \frac{1}{2}.

$$\frac{1}{3}xy^{4}z^{2}\times 2xy^{2}$$

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$\frac{2}{3}xy^{4}z^{2}xy^{2}$$

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

$$\frac{2}{3}x^{2}y^{4}z^{2}y^{2}$$

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

$$\frac{2}{3}x^{2}y^{6}z^{2}$$

Differentiate w.r.t. x

$$\frac{4xz^{2}y^{6}}{3}$$