Solve frac{25a^{2}b^{4}}{11x^{3}y^{7}}*66st^3/5abdiv2b^3/x^4y^6

$$\frac { 25 a ^ { 2 } b ^ { 4 } } { 11 x ^ { 3 } y ^ { 7 } } \times \frac { 66 s t ^ { 3 } } { 5 a b } \div \frac { 2 b ^ { 3 } } { x ^ { 4 } y ^ { 6 } }$$

Evaluate

$$\frac{15asxt^{3}}{y}$$

Solution Steps

Multiply \frac{25a^{2}b^{4}}{11x^{3}y^{7}} times \frac{66st^{3}}{5ab} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{25a^{2}b^{4}\times 66st^{3}}{11x^{3}y^{7}\times 5ab}}{\frac{2b^{3}}{x^{4}y^{6}}}$$

Cancel out 5\times 11ab in both numerator and denominator.

$$\frac{\frac{5\times 6asb^{3}t^{3}}{x^{3}y^{7}}}{\frac{2b^{3}}{x^{4}y^{6}}}$$

Divide \frac{5\times 6asb^{3}t^{3}}{x^{3}y^{7}} by \frac{2b^{3}}{x^{4}y^{6}} by multiplying \frac{5\times 6asb^{3}t^{3}}{x^{3}y^{7}} by the reciprocal of \frac{2b^{3}}{x^{4}y^{6}}.

$$\frac{5\times 6asb^{3}t^{3}x^{4}y^{6}}{x^{3}y^{7}\times 2b^{3}}$$

Cancel out 2b^{3}x^{3}y^{6} in both numerator and denominator.

$$\frac{3\times 5asxt^{3}}{y}$$

Multiply 3 and 5 to get 15.

$$\frac{15asxt^{3}}{y}$$

Differentiate w.r.t. x

$$\frac{15ast^{3}}{y}$$