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Algebra 1A
help please thank you

Algebra 1A help please thank you-example-1
User Portsample
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Answer:

To find the possible values of x that would result in a whole number simplification of the expression \(\sqrt[x]{441^{2}}\), we need to consider the factors of 441.

1. Prime factorize 441:

- 441 can be written as \(3^2 \times 7^2\).

2. Simplify the expression:

- \(\sqrt[x]{441^{2}}\) can be rewritten as \((3^2 \times 7^2)^{\frac{2}{x}}\).

- Using the properties of exponents, we can simplify further to \(3^{\frac{4}{x}} \times 7^{\frac{4}{x}}\).

3. Determine the values of x for which the exponents result in whole numbers:

- For the exponents to result in whole numbers, the denominator of \(\frac{4}{x}\) must be a factor of 4.

- The possible values for the denominator are 1, 2, and 4, as they are factors of 4.

4. Calculate the corresponding values of x:

- For each possible value of the denominator, we can solve for x by setting the denominator equal to the value and solving the equation: \(\frac{4}{x} = \text{denominator}\).

- For a denominator of 1, \(x = 4\).

- For a denominator of 2, \(x = 2\).

- For a denominator of 4, \(x = 1\).

Therefore, the possible values of x that would result in a whole number simplification of \(\sqrt[x]{441^{2}}\) are 4, 2, and 1.

Explanation:

Sorry for all of the symbols, I cant put in the equation properly so this is what it came out with when i typed it in- again, sorry for the mishap but here are the answers <33

User Durisvk
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