Solve (a^{4}+3a^{2}a^2)^2+(9a^4)^2

$$( a ^ { 4 } + 3 a ^ { 2 } a ^ { 2 } ) ^ { 2 } + ( 9 a ^ { 4 } ) ^ { 2 }$$

Evaluate

$$97a^{8}$$

Solution Steps

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

$$\left(a^{4}+3a^{4}\right)^{2}+\left(9a^{4}\right)^{2}$$

Combine a^{4} and 3a^{4} to get 4a^{4}.

$$\left(4a^{4}\right)^{2}+\left(9a^{4}\right)^{2}$$

Expand \left(4a^{4}\right)^{2}.

$$4^{2}\left(a^{4}\right)^{2}+\left(9a^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$4^{2}a^{8}+\left(9a^{4}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16a^{8}+\left(9a^{4}\right)^{2}$$

Expand \left(9a^{4}\right)^{2}.

$$16a^{8}+9^{2}\left(a^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$16a^{8}+9^{2}a^{8}$$

Calculate 9 to the power of 2 and get 81.

$$16a^{8}+81a^{8}$$

Combine 16a^{8} and 81a^{8} to get 97a^{8}.

$$97a^{8}$$

Expand

$$97a^{8}$$

Solution Steps

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

$$\left(a^{4}+3a^{4}\right)^{2}+\left(9a^{4}\right)^{2}$$

Combine a^{4} and 3a^{4} to get 4a^{4}.

$$\left(4a^{4}\right)^{2}+\left(9a^{4}\right)^{2}$$

Expand \left(4a^{4}\right)^{2}.

$$4^{2}\left(a^{4}\right)^{2}+\left(9a^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$4^{2}a^{8}+\left(9a^{4}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16a^{8}+\left(9a^{4}\right)^{2}$$

Expand \left(9a^{4}\right)^{2}.

$$16a^{8}+9^{2}\left(a^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$16a^{8}+9^{2}a^{8}$$

Calculate 9 to the power of 2 and get 81.

$$16a^{8}+81a^{8}$$

Combine 16a^{8} and 81a^{8} to get 97a^{8}.

$$97a^{8}$$