Solve 7*32x^3y/5xy^2*15y/8x^2y^4

$$7 \cdot \frac { 32 x ^ { 3 } y } { 5 x y ^ { 2 } } \cdot \frac { 15 y } { 8 x ^ { 2 } y ^ { 4 } }$$

Evaluate

$$\frac{84}{y^{4}}$$

Solution Steps

Cancel out xy in both numerator and denominator.

$$7\times \frac{32x^{2}}{5y}\times \frac{15y}{8x^{2}y^{4}}$$

Cancel out y in both numerator and denominator.

$$7\times \frac{32x^{2}}{5y}\times \frac{15}{8x^{2}y^{3}}$$

Express 7\times \frac{32x^{2}}{5y} as a single fraction.

$$\frac{7\times 32x^{2}}{5y}\times \frac{15}{8x^{2}y^{3}}$$

Multiply \frac{7\times 32x^{2}}{5y} times \frac{15}{8x^{2}y^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 32x^{2}\times 15}{5y\times 8x^{2}y^{3}}$$

Cancel out 5\times 8x^{2} in both numerator and denominator.

$$\frac{3\times 4\times 7}{yy^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{3\times 4\times 7}{y^{4}}$$

Multiply 3 and 4 to get 12.

$$\frac{12\times 7}{y^{4}}$$

Multiply 12 and 7 to get 84.

$$\frac{84}{y^{4}}$$

Differentiate w.r.t. y

$$-\frac{336}{y^{5}}$$