Solve 1/3x^6y^4z:1/2x^2y^3z=

$$\frac { 1 } { 3 } x ^ { 6 } y ^ { 4 } z : \frac { 1 } { 2 } x ^ { 2 } y ^ { 3 } z =$$

Evaluate

$$\frac{2z^{2}y^{7}x^{8}}{3}$$

Solution Steps

Divide \frac{1}{3}x^{6}y^{4}z by \frac{1}{2} by multiplying \frac{1}{3}x^{6}y^{4}z by the reciprocal of \frac{1}{2}.

$$\frac{1}{3}x^{6}y^{4}z\times 2x^{2}y^{3}z$$

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

$$\frac{2}{3}x^{6}y^{4}zx^{2}y^{3}z$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{2}{3}x^{8}y^{4}zy^{3}z$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{2}{3}x^{8}y^{7}zz$$

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

$$\frac{2}{3}x^{8}y^{7}z^{2}$$

Differentiate w.r.t. x

$$\frac{16z^{2}\left(xy\right)^{7}}{3}$$