Solve (2^3x^3y/y^2)^-2

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

Evaluate

$$\frac{y^{2}}{64x^{6}}$$

Solution Steps

Cancel out y in both numerator and denominator.

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

Calculate 2 to the power of 3 and get 8.

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

To raise \frac{8x^{3}}{y} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(8x^{3}\right)^{-2}.

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

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

$$\frac{8^{-2}x^{-6}}{y^{-2}}$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\frac{\frac{1}{64}x^{-6}}{y^{-2}}$$

Expand

$$\frac{y^{2}}{64x^{6}}$$

Solution Steps

Cancel out y in both numerator and denominator.

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

Calculate 2 to the power of 3 and get 8.

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

To raise \frac{8x^{3}}{y} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(8x^{3}\right)^{-2}.

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

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

$$\frac{8^{-2}x^{-6}}{y^{-2}}$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\frac{\frac{1}{64}x^{-6}}{y^{-2}}$$