Solve [y^2(3y^2)^2]^2

$$[ y ^ { 2 } ( 3 y ^ { 2 } ) ^ { 2 } ] ^ { 2 }$$

Evaluate

$$81y^{12}$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$\left(y^{2}\times 9y^{4}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\left(y^{6}\times 9\right)^{2}$$

Expand \left(y^{6}\times 9\right)^{2}.

$$\left(y^{6}\right)^{2}\times 9^{2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$y^{12}\times 9^{2}$$

Calculate 9 to the power of 2 and get 81.

$$y^{12}\times 81$$

Expand

$$81y^{12}$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$\left(y^{2}\times 9y^{4}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\left(y^{6}\times 9\right)^{2}$$

Expand \left(y^{6}\times 9\right)^{2}.

$$\left(y^{6}\right)^{2}\times 9^{2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$y^{12}\times 9^{2}$$

Calculate 9 to the power of 2 and get 81.

$$y^{12}\times 81$$