Question
is 10^-4 . 10^5 = to 1 tenth^-1
Answers
GPT-4o mini
To simplify \(10^{-4} \cdot 10^{5}\), you would add the exponents:
\[
10^{-4} \cdot 10^{5} = 10^{-4 + 5} = 10^{1} = 10
\]
Now, to evaluate \(1 \text{ tenth}^{-1}\):
The term "tenth" represents \(10^{-1}\), so:
\[
1 \text{ tenth}^{-1} = 1 \cdot (10^{-1})^{-1} = 1 \cdot 10^{1} = 10
\]
Therefore, we can see that:
\[
10^{-4} \cdot 10^{5} = 10 = 1 \text{ tenth}^{-1}
\]
So, yes, \(10^{-4} \cdot 10^{5} = 1 \text{ tenth}^{-1}\) is correct.
\[
10^{-4} \cdot 10^{5} = 10^{-4 + 5} = 10^{1} = 10
\]
Now, to evaluate \(1 \text{ tenth}^{-1}\):
The term "tenth" represents \(10^{-1}\), so:
\[
1 \text{ tenth}^{-1} = 1 \cdot (10^{-1})^{-1} = 1 \cdot 10^{1} = 10
\]
Therefore, we can see that:
\[
10^{-4} \cdot 10^{5} = 10 = 1 \text{ tenth}^{-1}
\]
So, yes, \(10^{-4} \cdot 10^{5} = 1 \text{ tenth}^{-1}\) is correct.