Solve frac{15x^{5}y^{8}}{21a^{7}b^{5}}:2x^3y^2/35a^10b^6

$$\frac { 15 x ^ { 5 } y ^ { 8 } } { 21 a ^ { 7 } b ^ { 5 } } : \frac { 2 x ^ { 3 } y ^ { 2 } } { 35 a ^ { 10 } b ^ { 6 } }$$

Evaluate

$$\frac{25bx^{2}a^{3}y^{6}}{2}$$

Solution Steps

Divide \frac{15x^{5}y^{8}}{21a^{7}b^{5}} by \frac{2x^{3}y^{2}}{35a^{10}b^{6}} by multiplying \frac{15x^{5}y^{8}}{21a^{7}b^{5}} by the reciprocal of \frac{2x^{3}y^{2}}{35a^{10}b^{6}}.

$$\frac{15x^{5}y^{8}\times 35a^{10}b^{6}}{21a^{7}b^{5}\times 2x^{3}y^{2}}$$

Cancel out 3\times 7y^{2}x^{3}b^{5}a^{7} in both numerator and denominator.

$$\frac{5\times 5bx^{2}a^{3}y^{6}}{2}$$

Multiply 5 and 5 to get 25.

$$\frac{25bx^{2}a^{3}y^{6}}{2}$$

Differentiate w.r.t. x

$$25bxa^{3}y^{6}$$