Solve (-2y^2x)^2div4yx^2

$$( - 2 y ^ { 2 } x ) ^ { 2 } \div 4 y x ^ { 2 }$$

Evaluate

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

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

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

$$\frac{4y^{4}x^{2}}{4}yx^{2}$$

Cancel out 4 and 4.

$$y^{4}x^{2}yx^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

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

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

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

Expand

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

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

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

$$\frac{4y^{4}x^{2}}{4}yx^{2}$$

Cancel out 4 and 4.

$$y^{4}x^{2}yx^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

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

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

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