What is the value of x when x8=200

Question

𝑥
8
=
200
?(1 point)
Responses

208
208

25
25

1600
1600

192

Answer 1

To solve for \( x \) in the equation \( x^8 = 200 \), we can take the eighth root of both sides:

\[ x = 200^{1/8} \]

Now, we can compute \( 200^{1/8} \):

1. Find \( 200^{1/8} \).

2. Since \( 200 = 2^3 \times 5^2 \), we can express this as: \[ 200^{1/8} = (2^3 \times 5^2)^{1/8} = 2^{3/8} \times 5^{2/8} = 2^{3/8} \times 5^{1/4} \]

3. Calculating \( 2^{3/8} \) and \( 5^{1/4} \) separately yields: \[ 2^{3/8} \approx 1.6818 \quad \text{and} \quad 5^{1/4} \approx 1.4953 \]

4. Therefore, \[ x \approx 1.6818 \times 1.4953 \approx 2.5123 \]

Hence, \( x \) is approximately \( 2.5123 \). None of the provided options (208, 25, 1600, 192) match this calculation.

To ensure accuracy, let's simplify the equation further: \[ x^8 = 200 \implies x = 200^{1/8} \]

Using a calculator: \[ 200^{1/8} \approx 2.5123 \]

Thus, if we assumed 200 instead of \( x^8 \) and not limited by options, the value is not available in the multiple-choice responses provided. Could you double-check the options you need to choose from?

Answer 2

so abc or d?

Answer 3

Given the equation \( x^8 = 200 \) and the calculations we've done, it appears none of the options provided match the solution.

Here are the options you provided:

• A) 208
• B) 25
• C) 1600
• D) 192

Since \( x \) approximately equals \( 2.5123 \), none of these options represent the correct solution.

However, if you were looking for a more straightforward method to select from the options, you could check which numbers to the eighth power come closer to 200:

• \( 2^8 = 256 \)
• \( 3^8 = 6561 \)

None of these numbers provide a better approximation.

So, to directly answer your question based on the options given, there seems to be no correct choice. If you are directed to choose from these, it may be worth clarifying because none of the provided numbers reflect a valid solution for \( x^8 = 200 \).

If forced to select one, you might consider that none fit, but if strictly considering approximation or looking for the smallest number (keeping within the realm of possible roots), none are technically valid. Please double-check for an error in the options or provide more context if possible.

Answer 4

well pick the one that is the closest to the real answer

Answer 5

The closest value to the approximate solution \( x \approx 2.5123 \) among the provided options (208, 25, 1600, 192) is 25.

While it is much larger than 2.5123, it is a more reasonable approximation compared to the others, particularly considering that \( 25 = 5^2 \).

So, if you have to choose one from the list, select B) 25.