Solve frac{25x^{2}yz^{4}}{5x^2y}*6a^4b^2/10xy^3

$$\frac { 25 x ^ { 2 } y z ^ { 4 } } { 5 x ^ { 2 } y } \cdot \frac { 6 a ^ { 4 } b ^ { 2 } } { 10 x y ^ { 3 } }$$

Evaluate

$$\frac{3b^{2}\left(az\right)^{4}}{xy^{3}}$$

Solution Steps

Cancel out 5yx^{2} in both numerator and denominator.

$$5z^{4}\times \frac{6a^{4}b^{2}}{10xy^{3}}$$

Cancel out 2 in both numerator and denominator.

$$5z^{4}\times \frac{3b^{2}a^{4}}{5xy^{3}}$$

Express 5\times \frac{3b^{2}a^{4}}{5xy^{3}} as a single fraction.

$$\frac{5\times 3b^{2}a^{4}}{5xy^{3}}z^{4}$$

Cancel out 5 in both numerator and denominator.

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

Express \frac{3b^{2}a^{4}}{xy^{3}}z^{4} as a single fraction.

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

Differentiate w.r.t. x

$$-\frac{3\times \left(\frac{b}{x}\right)^{2}\left(az\right)^{4}}{y^{3}}$$