Solve the equation. There are two real solutions. x ^ 2 = 7 ^ 8 .

Question

-7,7
- 7 ^ 4, 7 ^ 4
sqrt(8), - sqrt(8)
- 7 ^ 2, 7 ^ 2

Answer 1

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

When we do so, we get:

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

Using the property of exponents, we can simplify \( \sqrt{7^8} \):

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

So, the solutions to the equation are:

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

Thus, the two real solutions are:

• \( -7^4 \)
• \( 7^4 \)

So the correct answer is:

• \( -7^4, 7^4 \)