Question

Which expression is equivalent to 2 (5) Superscript 4?
2 times 5 times 4
2 times 5 times 5 times 5 times 5
2 times 4 times 4 times 4 times 4 times 4
10 times 10 times 10 times 10

Answer 1

To simplify the expression \(2 \times 5^4\), we first evaluate \(5^4\).

Calculating \(5^4\):
\[
5^4 = 5 \times 5 \times 5 \times 5
\]
Now we evaluate \(5 \times 5 = 25\), then \(25 \times 5 = 125\), and finally \(125 \times 5 = 625\).
So, \(5^4 = 625\).

Now we multiply that by 2:
\[
2 \times 625 = 1250
\]

Now we can analyze the answer choices based on our expression:

1. **2 times 5 times 4**:
\[
2 \times 5 \times 4 = 40 \quad (\text{not equal to } 1250)
\]

2. **2 times 5 times 5 times 5 times 5**:
\[
2 \times 5 \times 5 \times 5 \times 5 = 2 \times 625 = 1250 \quad (\text{this matches})
\]

3. **2 times 4 times 4 times 4 times 4 times 4**:
\[
2 \times 4^5 = 2 \times 1024 = 2048 \quad (\text{not equal to } 1250)
\]

4. **10 times 10 times 10 times 10**:
\[
10^4 = 10000 \quad (\text{not equal to } 1250)
\]

Therefore, the expression that is equivalent to \(2 \times 5^4\) is:
\[
\text{2 times 5 times 5 times 5 times 5}
\]