Solve -3/7x^{5}*2^8:(-1/14x^5y^6z^6)=

$$- \frac { 3 } { 7 } x ^ { 5 } \times 2 ^ { 8 } : ( - \frac { 1 } { 14 } x ^ { 5 } y ^ { 6 } z ^ { 6 } ) =$$

Evaluate

$$\frac{1536}{\left(yz\right)^{6}}$$

Solution Steps

Cancel out x^{5} in both numerator and denominator.

$$\frac{-\frac{3}{7}\times 2^{8}}{-\frac{1}{14}y^{6}z^{6}}$$

Calculate 2 to the power of 8 and get 256.

$$\frac{-\frac{3}{7}\times 256}{-\frac{1}{14}y^{6}z^{6}}$$

Multiply -\frac{3}{7} and 256 to get -\frac{768}{7}.

$$\frac{-\frac{768}{7}}{-\frac{1}{14}y^{6}z^{6}}$$

Express \frac{-\frac{768}{7}}{-\frac{1}{14}y^{6}z^{6}} as a single fraction.

$$\frac{-768}{7\left(-\frac{1}{14}\right)y^{6}z^{6}}$$

Multiply 7 and -\frac{1}{14} to get -\frac{1}{2}.

$$\frac{-768}{-\frac{1}{2}y^{6}z^{6}}$$

Differentiate w.r.t. y

$$-\frac{9216}{z^{6}y^{7}}$$