Question
What is the exponent in an equivalent form to the expression 11⋅13
if the base is 1?(1 point)
Remaining Attempts : 3
if the base is 1?(1 point)
Remaining Attempts : 3
Answers
Answered by
GPT-4o mini
In exponential notation, when you express a number in terms of a base and an exponent, the number can be represented as \( b^n \), where \( b \) is the base and \( n \) is the exponent.
If the base is 1, any number can be written as \( 1^n \) for any exponent \( n \). This means that regardless of the value of \( n \), \( 1^n \) will always equal 1.
When looking for an exponent that makes \( 11 \cdot 13 \) equivalent to a base of 1, we note that:
\[
11 \cdot 13 = 143
\]
To express 143 in terms of base 1, it can theoretically be expressed as:
\[
143 = 1^x
\]
However, for this to hold, \( x \) must be 0 because:
\[
1^0 = 1
\]
In conclusion, since there is no way to express 143 as \( 1^n \) for a finite \( n \) where \( n \) is not 0, the correct interpretation is that no finite exponent will suffice.
The simple answer is that if you are looking for the exponent in terms of base 1 representation, it's not applicable in practical terms because \( 1^n \) will always yield 1, regardless of \( n \).
So, in this context, the answer to your question regarding the exponent is: **0** (if you're considering that \( 1^0 = 1 \)). However, remember that this means we are moving away from the original value of \( 11 \cdot 13 = 143 \) since it can never equal 1 as per this method.
If the base is 1, any number can be written as \( 1^n \) for any exponent \( n \). This means that regardless of the value of \( n \), \( 1^n \) will always equal 1.
When looking for an exponent that makes \( 11 \cdot 13 \) equivalent to a base of 1, we note that:
\[
11 \cdot 13 = 143
\]
To express 143 in terms of base 1, it can theoretically be expressed as:
\[
143 = 1^x
\]
However, for this to hold, \( x \) must be 0 because:
\[
1^0 = 1
\]
In conclusion, since there is no way to express 143 as \( 1^n \) for a finite \( n \) where \( n \) is not 0, the correct interpretation is that no finite exponent will suffice.
The simple answer is that if you are looking for the exponent in terms of base 1 representation, it's not applicable in practical terms because \( 1^n \) will always yield 1, regardless of \( n \).
So, in this context, the answer to your question regarding the exponent is: **0** (if you're considering that \( 1^0 = 1 \)). However, remember that this means we are moving away from the original value of \( 11 \cdot 13 = 143 \) since it can never equal 1 as per this method.