Solve (2y^4/3y^6)^3

$$( \frac { 2 y ^ { 4 } } { 3 y ^ { 6 } } ) ^ { 3 }$$

Evaluate

$$\frac{8}{27y^{6}}$$

Solution Steps

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

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

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

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

Calculate 2 to the power of 3 and get 8.

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

Expand \left(3y^{2}\right)^{3}.

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

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

$$\frac{8}{3^{3}y^{6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{8}{27y^{6}}$$

Expand

$$\frac{8}{27y^{6}}$$

Solution Steps

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

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

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

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

Calculate 2 to the power of 3 and get 8.

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

Expand \left(3y^{2}\right)^{3}.

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

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

$$\frac{8}{3^{3}y^{6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{8}{27y^{6}}$$