Solve (2x^3y^4/-xy^3*-x)^4

$$( \frac { 2 x ^ { 3 } y ^ { 4 } } { - x y ^ { 3 } } \cdot - x ) ^ { 4 }$$

Evaluate

$$16y^{4}x^{12}$$

Solution Steps

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

$$\left(\frac{2yx^{3}}{-x}\left(-x\right)\right)^{4}$$

Express \frac{2yx^{3}}{-x}\left(-x\right) as a single fraction.

$$\left(\frac{-2yx^{3}x}{-x}\right)^{4}$$

To raise \frac{-2yx^{3}x}{-x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-2yx^{3}x\right)^{4}}{\left(-x\right)^{4}}$$

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

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

Expand \left(-2yx^{4}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{\left(-2\right)^{4}y^{4}x^{16}}{\left(-x\right)^{4}}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{16y^{4}x^{16}}{\left(-x\right)^{4}}$$

Expand \left(-x\right)^{4}.

$$\frac{16y^{4}x^{16}}{\left(-1\right)^{4}x^{4}}$$

Calculate -1 to the power of 4 and get 1.

$$\frac{16y^{4}x^{16}}{1x^{4}}$$

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

$$16y^{4}x^{12}$$

Expand

$$16y^{4}x^{12}$$

Solution Steps

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

$$\left(\frac{2yx^{3}}{-x}\left(-x\right)\right)^{4}$$

Express \frac{2yx^{3}}{-x}\left(-x\right) as a single fraction.

$$\left(\frac{-2yx^{3}x}{-x}\right)^{4}$$

To raise \frac{-2yx^{3}x}{-x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-2yx^{3}x\right)^{4}}{\left(-x\right)^{4}}$$

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

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

Expand \left(-2yx^{4}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{\left(-2\right)^{4}y^{4}x^{16}}{\left(-x\right)^{4}}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{16y^{4}x^{16}}{\left(-x\right)^{4}}$$

Expand \left(-x\right)^{4}.

$$\frac{16y^{4}x^{16}}{\left(-1\right)^{4}x^{4}}$$

Calculate -1 to the power of 4 and get 1.

$$\frac{16y^{4}x^{16}}{1x^{4}}$$

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

$$16y^{4}x^{12}$$