Solve x^2 = 7^8 by inspection there are two real solutions enter the lesser number first and use exponents in your responses

Answer 1

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

Taking the square root gives us:

\[ x = \pm 7^4 \]

Calculating \(7^4\):

\[ 7^4 = (7^2)^2 = 49^2 = 2401 \]

Thus, the two real solutions are:

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

So the lesser number first is:

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

In exponent form, the solutions are:

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