Solve left(-2xyright)^210x^3y^11/8x^10{y^4}

$$\frac{ { \left(-2xy \right) }^{ 2 } 10 { x }^{ 3 } { y }^{ 11 } }{ 8 { x }^{ 10 } { y }^{ 4 } }$$

Evaluate

$$\frac{5y^{9}}{x^{5}}$$

Solution Steps

Cancel out 2x^{3}y^{4} in both numerator and denominator.

$$\frac{5\left(-2xy\right)^{2}y^{7}}{4x^{7}}$$

Expand \left(-2xy\right)^{2}.

$$\frac{5\left(-2\right)^{2}x^{2}y^{2}y^{7}}{4x^{7}}$$

Calculate -2 to the power of 2 and get 4.

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

Multiply 5 and 4 to get 20.

$$\frac{20x^{2}y^{2}y^{7}}{4x^{7}}$$

To multiply powers of the same base, add their exponents. Add 2 and 7 to get 9.

$$\frac{20x^{2}y^{9}}{4x^{7}}$$

Cancel out 4x^{2} in both numerator and denominator.

$$\frac{5y^{9}}{x^{5}}$$

Expand

$$\frac{5y^{9}}{x^{5}}$$

Solution Steps

Cancel out 2x^{3}y^{4} in both numerator and denominator.

$$\frac{5\left(-2xy\right)^{2}y^{7}}{4x^{7}}$$

Expand \left(-2xy\right)^{2}.

$$\frac{5\left(-2\right)^{2}x^{2}y^{2}y^{7}}{4x^{7}}$$

Calculate -2 to the power of 2 and get 4.

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

Multiply 5 and 4 to get 20.

$$\frac{20x^{2}y^{2}y^{7}}{4x^{7}}$$

To multiply powers of the same base, add their exponents. Add 2 and 7 to get 9.

$$\frac{20x^{2}y^{9}}{4x^{7}}$$

Cancel out 4x^{2} in both numerator and denominator.

$$\frac{5y^{9}}{x^{5}}$$