Solve {l}{(5x^2)^2}{+(20x^2)^2}

$$\left. \begin{array} { l } { ( 5 x ^ { 2 } ) ^ { 2 } } \\ { + ( 20 x ^ { 2 } ) ^ { 2 } } \end{array} \right.$$

Evaluate

$$425x^{4}$$

Solution Steps

Expand \left(5x^{2}\right)^{2}.

$$5^{2}\left(x^{2}\right)^{2}+\left(20x^{2}\right)^{2}$$

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

$$5^{2}x^{4}+\left(20x^{2}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25x^{4}+\left(20x^{2}\right)^{2}$$

Expand \left(20x^{2}\right)^{2}.

$$25x^{4}+20^{2}\left(x^{2}\right)^{2}$$

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

$$25x^{4}+20^{2}x^{4}$$

Calculate 20 to the power of 2 and get 400.

$$25x^{4}+400x^{4}$$

Combine 25x^{4} and 400x^{4} to get 425x^{4}.

$$425x^{4}$$

Expand

$$425x^{4}$$

Solution Steps

Expand \left(5x^{2}\right)^{2}.

$$5^{2}\left(x^{2}\right)^{2}+\left(20x^{2}\right)^{2}$$

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

$$5^{2}x^{4}+\left(20x^{2}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25x^{4}+\left(20x^{2}\right)^{2}$$

Expand \left(20x^{2}\right)^{2}.

$$25x^{4}+20^{2}\left(x^{2}\right)^{2}$$

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

$$25x^{4}+20^{2}x^{4}$$

Calculate 20 to the power of 2 and get 400.

$$25x^{4}+400x^{4}$$

Combine 25x^{4} and 400x^{4} to get 425x^{4}.

$$425x^{4}$$