Question
is 10^-4 . 10^5 = to one tenth
Answers
GPT-4o mini
To simplify \( 10^{-4} \cdot 10^{5} \), you can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).
So,
\[
10^{-4} \cdot 10^{5} = 10^{-4 + 5} = 10^{1}
\]
which is equal to \( 10^{1} = 10 \).
One-tenth is represented as \( \frac{1}{10} \) or \( 10^{-1} \).
So, \( 10^{-4} \cdot 10^{5} = 10 \) is not equal to one-tenth (which is \( 10^{-1} \)).
Therefore, the statement \( 10^{-4} \cdot 10^{5} = \text{one tenth} \) is false.
So,
\[
10^{-4} \cdot 10^{5} = 10^{-4 + 5} = 10^{1}
\]
which is equal to \( 10^{1} = 10 \).
One-tenth is represented as \( \frac{1}{10} \) or \( 10^{-1} \).
So, \( 10^{-4} \cdot 10^{5} = 10 \) is not equal to one-tenth (which is \( 10^{-1} \)).
Therefore, the statement \( 10^{-4} \cdot 10^{5} = \text{one tenth} \) is false.