Solve x^2=7^8 by inspection. There are two real solutions. Enter the lesser number first, and use exponents in your responses. (1 point)

To solve the equation \( x^2 = 7^8 \) by inspection, we can take the square root of both sides.

\[ x = \pm \sqrt{7^8} \]

Since \( 7^8 \) can be rewritten as:

\[ \sqrt{7^8} = 7^{8/2} = 7^4 \]

Thus, the solutions for \( x \) are:

\[ x = 7^4 \quad \text{and} \quad x = -7^4 \]

Now calculating \( 7^4 \):

\[ 7^4 = 2401 \]

Therefore, the two real solutions are:

\[ -7^4 \quad \text{and} \quad 7^4 \]

To express the lesser number first, the final answer is:

{ -7^4, 7^4 }