Question
what is the exponent in an equivalent form to the expression 1 to the power of 1 times 1 to the power f 3 if the base is 1
Answers
Answered by
GPT-4o mini
To simplify the expression \(1^1 \cdot 1^f \cdot 3\), we can start by evaluating the individual components.
1. The expression \(1^1 = 1\).
2. The expression \(1^f = 1\) for any value of \(f\) (since any number raised to any power equals 1 when the base is 1).
3. Therefore, the product \(1^1 \cdot 1^f = 1 \cdot 1 = 1\).
So, if we consider the overall expression including the 3, we have:
\[
1 \cdot 3 = 3.
\]
Thus, any expression involving \(1\) as a base raised to any power will always evaluate to \(1\), and the multiplication by \(3\) does not change the conclusion about the exponent.
If the question is asking about an equivalent form involving exponents, we could say:
\[
1^x = 1 \text{ for any } x.
\]
However, the exponent itself does not influence the outcome in this case.
In summary, while the expression \(1^1 \cdot 1^f \cdot 3\) simplifies to \(3\), the exponent part \(1^x\) remains \(1\) for any power \(x\).
1. The expression \(1^1 = 1\).
2. The expression \(1^f = 1\) for any value of \(f\) (since any number raised to any power equals 1 when the base is 1).
3. Therefore, the product \(1^1 \cdot 1^f = 1 \cdot 1 = 1\).
So, if we consider the overall expression including the 3, we have:
\[
1 \cdot 3 = 3.
\]
Thus, any expression involving \(1\) as a base raised to any power will always evaluate to \(1\), and the multiplication by \(3\) does not change the conclusion about the exponent.
If the question is asking about an equivalent form involving exponents, we could say:
\[
1^x = 1 \text{ for any } x.
\]
However, the exponent itself does not influence the outcome in this case.
In summary, while the expression \(1^1 \cdot 1^f \cdot 3\) simplifies to \(3\), the exponent part \(1^x\) remains \(1\) for any power \(x\).