Question
Simplify: 125 to the power 3
A.
25
B.
5
C.
15
D.
10
A.
25
B.
5
C.
15
D.
10
Answers
GPT-4o mini
To simplify \(125^3\):
First, note that \(125 = 5^3\). Therefore, we can rewrite \(125^3\) as:
\[
(5^3)^3 = 5^{3 \cdot 3} = 5^9
\]
Now, to find the exact numerical value of \(5^9\):
1. Calculate \(5^2 = 25\)
2. Calculate \(5^3 = 125\)
3. Calculate \(5^4 = 625\)
4. Calculate \(5^5 = 3125\)
5. Calculate \(5^6 = 15625\)
6. Calculate \(5^7 = 78125\)
7. Calculate \(5^8 = 390625\)
8. Calculate \(5^9 = 1953125\)
However, the options listed (25, 5, 15, 10) do not correspond to the result of \(125^3\) being \(1953125\).
Since we only need to simplify \(125^3\) itself, we can leave it as is or conclude that it is not represented in the given options. None of the options directly apply in this case.
If looking for a reduced numerical base form, \(125^{1/3} = 5\). Thus \(125^{1/3} = 5\) can match the option \(B: 5\) in a context of seeking cube roots instead.
So, revisiting the options and aiming for simplifications aligning with powers and roots, the perhaps most suitable choice is \(B: 5\). However, please be aware that \(125^3 = 1953125\) is the actual result.
First, note that \(125 = 5^3\). Therefore, we can rewrite \(125^3\) as:
\[
(5^3)^3 = 5^{3 \cdot 3} = 5^9
\]
Now, to find the exact numerical value of \(5^9\):
1. Calculate \(5^2 = 25\)
2. Calculate \(5^3 = 125\)
3. Calculate \(5^4 = 625\)
4. Calculate \(5^5 = 3125\)
5. Calculate \(5^6 = 15625\)
6. Calculate \(5^7 = 78125\)
7. Calculate \(5^8 = 390625\)
8. Calculate \(5^9 = 1953125\)
However, the options listed (25, 5, 15, 10) do not correspond to the result of \(125^3\) being \(1953125\).
Since we only need to simplify \(125^3\) itself, we can leave it as is or conclude that it is not represented in the given options. None of the options directly apply in this case.
If looking for a reduced numerical base form, \(125^{1/3} = 5\). Thus \(125^{1/3} = 5\) can match the option \(B: 5\) in a context of seeking cube roots instead.
So, revisiting the options and aiming for simplifications aligning with powers and roots, the perhaps most suitable choice is \(B: 5\). However, please be aware that \(125^3 = 1953125\) is the actual result.