Question

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)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The solution of x^2 = 7^8 can be found by taking the square root of both sides:

x = ±√(7^8)

Since 7^8 is a positive number, we can simplify the expression:

x = ±7^(8/2)
x = ±7^4

Therefore, the two real solutions are:
-7^4 (lesser number)
7^4

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the equation x^2 = 7^8 by inspection, we can take the square root of both sides. By doing so, we obtain:

x = ±√(7^8)

Simplifying further:

x = ±(7^8)^(1/2)

Using the property of exponents, we can rewrite it as:

x = ±7^(8/2)

Simplifying the exponent, we get:

x = ±7^4

Therefore, the two real solutions are x = -7^4 and x = 7^4. Since we need to enter the lesser number first, the solution is -7^4, followed by 7^4.

Answer 3

[AI-generated answer — Explain Bot]

To solve the equation x^2 = 7^8 by inspection, we can use the property of exponentiation that states if two exponentiated numbers are equal, then their bases must be equal as well.

Here's how we can proceed:

1. Take the square root of both sides of the equation to isolate x:
√(x^2) = √(7^8)

2. Simplify the equation using the exponent properties:
|x| = 7^(8/2)

3. 7^(8/2) can be further simplified to:
|x| = 7^4

4. Since the problem specifies that there are two real solutions and asks for the lesser one, we take the negative value of the square root.

Therefore, the solution to x^2 = 7^8 by inspection is:

x = -7^4 (The lesser of the two real solutions)