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

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

Evaluate

$$\frac{y}{24}$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$\frac{9y^{4}}{\left(6y\right)^{3}}$$

Expand \left(6y\right)^{3}.

$$\frac{9y^{4}}{6^{3}y^{3}}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{9y^{4}}{216y^{3}}$$

Cancel out 9y^{3} in both numerator and denominator.

$$\frac{y}{24}$$

Expand

$$\frac{y}{24}$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$\frac{9y^{4}}{\left(6y\right)^{3}}$$

Expand \left(6y\right)^{3}.

$$\frac{9y^{4}}{6^{3}y^{3}}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{9y^{4}}{216y^{3}}$$

Cancel out 9y^{3} in both numerator and denominator.

$$\frac{y}{24}$$