Question
An equation with a missing exponent is shown.
1
125
=
5
n
125
1
= 5
n
What is the value of the missing exponent
n
n ?
1
125
=
5
n
125
1
= 5
n
What is the value of the missing exponent
n
n ?
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve for the missing exponent \( n \) in the equation
\[
\frac{1}{125} = 5^n,
\]
we first rewrite \( 125 \) in terms of base \( 5 \). We know that
\[
125 = 5^3.
\]
Therefore,
\[
\frac{1}{125} = \frac{1}{5^3} = 5^{-3}.
\]
Now, we can rewrite the equation as:
\[
5^{-3} = 5^n.
\]
Since the bases are the same, we can equate the exponents:
\[
-3 = n.
\]
Thus, the value of the missing exponent \( n \) is
\[
\boxed{-3}.
\]
\[
\frac{1}{125} = 5^n,
\]
we first rewrite \( 125 \) in terms of base \( 5 \). We know that
\[
125 = 5^3.
\]
Therefore,
\[
\frac{1}{125} = \frac{1}{5^3} = 5^{-3}.
\]
Now, we can rewrite the equation as:
\[
5^{-3} = 5^n.
\]
Since the bases are the same, we can equate the exponents:
\[
-3 = n.
\]
Thus, the value of the missing exponent \( n \) is
\[
\boxed{-3}.
\]
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