Solve (3x^4)^2+(2x^2)^4

$$( 3 x ^ { 4 } ) ^ { 2 } + ( 2 x ^ { 2 } ) ^ { 4 }$$

Evaluate

$$25x^{8}$$

Solution Steps

Expand \left(3x^{4}\right)^{2}.

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

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

$$3^{2}x^{8}+\left(2x^{2}\right)^{4}$$

Calculate 3 to the power of 2 and get 9.

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

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

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

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

$$9x^{8}+2^{4}x^{8}$$

Calculate 2 to the power of 4 and get 16.

$$9x^{8}+16x^{8}$$

Combine 9x^{8} and 16x^{8} to get 25x^{8}.

$$25x^{8}$$

Expand

$$25x^{8}$$

Solution Steps

Expand \left(3x^{4}\right)^{2}.

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

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

$$3^{2}x^{8}+\left(2x^{2}\right)^{4}$$

Calculate 3 to the power of 2 and get 9.

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

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

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

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

$$9x^{8}+2^{4}x^{8}$$

Calculate 2 to the power of 4 and get 16.

$$9x^{8}+16x^{8}$$

Combine 9x^{8} and 16x^{8} to get 25x^{8}.

$$25x^{8}$$