Solve 16x^2/y^4*5x^2/4y^2

$$\frac { 16 x ^ { 2 } } { y ^ { 4 } } \cdot \frac { 5 x ^ { 2 } } { 4 y ^ { 2 } }$$

Evaluate

$$\frac{20x^{4}}{y^{6}}$$

Solution Steps

Multiply \frac{16x^{2}}{y^{4}} times \frac{5x^{2}}{4y^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16x^{2}\times 5x^{2}}{y^{4}\times 4y^{2}}$$

Cancel out 4 in both numerator and denominator.

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

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

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

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

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

Multiply 4 and 5 to get 20.

$$\frac{20x^{4}}{y^{6}}$$

Differentiate w.r.t. x

$$\frac{80x^{3}}{y^{6}}$$