Solve frac{(-2xy)^{2}*2(x^2y^-1)^3}{8(xy)^-3}

$$\frac { ( - 2 x y ) ^ { 2 } \times 2 ( x ^ { 2 } y ^ { - 1 } ) ^ { 3 } } { 8 ( x y ) ^ { - 3 } }$$

Evaluate

$$y^{2}x^{11}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{\left(\frac{1}{y}x^{2}\right)^{3}\left(-2xy\right)^{2}}{4\left(xy\right)^{-3}}$$

Express \frac{1}{y}x^{2} as a single fraction.

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

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

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

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

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

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

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

Express \frac{\left(x^{2}\right)^{3}}{y^{3}}\times 4 as a single fraction.

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

Express \frac{\left(x^{2}\right)^{3}\times 4}{y^{3}}x^{2} as a single fraction.

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

Express \frac{\left(x^{2}\right)^{3}\times 4x^{2}}{y^{3}}y^{2} as a single fraction.

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

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

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

Expand \left(xy\right)^{-3}.

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

Express \frac{\frac{4x^{2}\left(x^{2}\right)^{3}}{y}}{4x^{-3}y^{-3}} as a single fraction.

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

Cancel out 4 in both numerator and denominator.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{x^{5}\left(x^{2}\right)^{3}}{y^{-3}y}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{x^{5}x^{6}}{y^{-3}y}$$

To multiply powers of the same base, add their exponents. Add 5 and 6 to get 11.

$$\frac{x^{11}}{y^{-3}y}$$

To multiply powers of the same base, add their exponents. Add -3 and 1 to get -2.

$$\frac{x^{11}}{y^{-2}}$$

Expand

$$y^{2}x^{11}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{\left(\frac{1}{y}x^{2}\right)^{3}\left(-2xy\right)^{2}}{4\left(xy\right)^{-3}}$$

Express \frac{1}{y}x^{2} as a single fraction.

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

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

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

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

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

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

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

Express \frac{\left(x^{2}\right)^{3}}{y^{3}}\times 4 as a single fraction.

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

Express \frac{\left(x^{2}\right)^{3}\times 4}{y^{3}}x^{2} as a single fraction.

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

Express \frac{\left(x^{2}\right)^{3}\times 4x^{2}}{y^{3}}y^{2} as a single fraction.

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

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

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

Expand \left(xy\right)^{-3}.

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

Express \frac{\frac{4x^{2}\left(x^{2}\right)^{3}}{y}}{4x^{-3}y^{-3}} as a single fraction.

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

Cancel out 4 in both numerator and denominator.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{x^{5}\left(x^{2}\right)^{3}}{y^{-3}y}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{x^{5}x^{6}}{y^{-3}y}$$

To multiply powers of the same base, add their exponents. Add 5 and 6 to get 11.

$$\frac{x^{11}}{y^{-3}y}$$

To multiply powers of the same base, add their exponents. Add -3 and 1 to get -2.

$$\frac{x^{11}}{y^{-2}}$$