Question
What is the exponent in an equivalent form to the expression 1 with exponent of 1 times 1 with exponent of 3 if the base is one?
Answers
GPT-4o mini
To find the exponent in an equivalent form to the expression \( 1^1 \times 1^3 \), we start by simplifying the expression:
1. Recall that any non-zero number raised to a power is equal to itself. Thus, we have:
\[
1^1 = 1
\]
and
\[
1^3 = 1.
\]
2. Now, multiply these two results:
\[
1^1 \times 1^3 = 1 \times 1 = 1.
\]
3. Since the product is \( 1 \), we can express this in an equivalent form using exponents:
\[
1 = 1^x
\]
for any exponent \( x \).
In conclusion, since \( 1 \) raised to any power is still \( 1 \), there is no specific exponent that uniquely represents the equivalent form except that it can be expressed as \( 1^x \) for any \( x \). Thus, we can say that the exponent is **any real number** (commonly denoted as \( x \)).
1. Recall that any non-zero number raised to a power is equal to itself. Thus, we have:
\[
1^1 = 1
\]
and
\[
1^3 = 1.
\]
2. Now, multiply these two results:
\[
1^1 \times 1^3 = 1 \times 1 = 1.
\]
3. Since the product is \( 1 \), we can express this in an equivalent form using exponents:
\[
1 = 1^x
\]
for any exponent \( x \).
In conclusion, since \( 1 \) raised to any power is still \( 1 \), there is no specific exponent that uniquely represents the equivalent form except that it can be expressed as \( 1^x \) for any \( x \). Thus, we can say that the exponent is **any real number** (commonly denoted as \( x \)).