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

Answer 1

To solve the equation \( x^2 = 7^8 \), we take the square root of both sides. This gives us:

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

Recall that \( \sqrt{a^b} = a^{b/2} \), so we can simplify \( \sqrt{7^8} \):

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

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

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

Calculating \( 7^4 \):

\[ 7^4 = 2401 \]

Therefore, the two real solutions are:

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

The lesser solution is:

\[ -7^4 \]

So, the final answers are:

\[ -7^4, \quad 7^4 \]