Solve 5x^{6}y^5*3/2xy^3div5/2x^2y^4

$$5 x ^ { 6 } y ^ { 5 } \times \frac { 3 } { 2 x y ^ { 3 } } \div \frac { 5 } { 2 } x ^ { 2 } y ^ { 4 }$$

Evaluate

$$3y^{6}x^{7}$$

Solution Steps

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

$$\frac{\frac{5\times 3}{2xy^{3}}x^{6}y^{5}}{\frac{5}{2}}x^{2}y^{4}$$

Multiply 5 and 3 to get 15.

$$\frac{\frac{15}{2xy^{3}}x^{6}y^{5}}{\frac{5}{2}}x^{2}y^{4}$$

Express \frac{15}{2xy^{3}}x^{6} as a single fraction.

$$\frac{\frac{15x^{6}}{2xy^{3}}y^{5}}{\frac{5}{2}}x^{2}y^{4}$$

Cancel out x in both numerator and denominator.

$$\frac{\frac{15x^{5}}{2y^{3}}y^{5}}{\frac{5}{2}}x^{2}y^{4}$$

Express \frac{15x^{5}}{2y^{3}}y^{5} as a single fraction.

$$\frac{\frac{15x^{5}y^{5}}{2y^{3}}}{\frac{5}{2}}x^{2}y^{4}$$

Cancel out y^{3} in both numerator and denominator.

$$\frac{\frac{15y^{2}x^{5}}{2}}{\frac{5}{2}}x^{2}y^{4}$$

Divide \frac{15y^{2}x^{5}}{2} by \frac{5}{2} by multiplying \frac{15y^{2}x^{5}}{2} by the reciprocal of \frac{5}{2}.

$$\frac{15y^{2}x^{5}\times 2}{2\times 5}x^{2}y^{4}$$

Cancel out 2\times 5 in both numerator and denominator.

$$3y^{2}x^{5}x^{2}y^{4}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$3y^{2}x^{7}y^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$3y^{6}x^{7}$$

Differentiate w.r.t. x

$$21\left(xy\right)^{6}$$