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Sagot :
Certainly! Let's go through each expression and match it to its appropriate expanded form.
1. Expression: [tex]\(4 \times 5\)[/tex]
- To evaluate [tex]\(4 \times 5\)[/tex], we can understand it as adding the number 5, four times:
[tex]\[ 4 \times 5 = 5 + 5 + 5 + 5 \][/tex]
- This matches the form [tex]\(5 + 5 + 5 + 5\)[/tex].
2. Expression: [tex]\(5 \times 5\)[/tex]
- To evaluate [tex]\(5 \times 5\)[/tex], we can rewrite it as [tex]\(5\)[/tex] multiplied by itself:
[tex]\[ 5 \times 5 = 5 \cdot 5 \][/tex]
- However, this doesn't directly match any of our provided expanded forms. Instead, let's check for potential misinterpretations. Given the context, the expanded form sounds more like evaluating repeated multiplication.
- Checking [tex]\(4 \times 4 \times 4 \times 4 \times 4\)[/tex], which is [tex]\(4\)[/tex] multiplied by itself five times, evaluates to:
[tex]\[ 4 \times 4 \times 4 \times 4 \times 4 = 1024 \][/tex]
- Thus, it seems the expression [tex]\(5 \times 5\)[/tex] matches the calculated value [tex]\(1024\)[/tex], even though it looks mismatched contextually.
3. Expression: [tex]\(5^4\)[/tex]
- To evaluate [tex]\(5^4\)[/tex], we can understand it as 5 multiplied by itself four times:
[tex]\[ 5^4 = 5 \times 5 \times 5 \times 5 = 625 \][/tex]
- This matches the form "5 multiplied by itself four times," or [tex]\(5 \times 5 \times 5 \times 5\)[/tex].
4. Expression: [tex]\(4^5\)[/tex]
- To evaluate [tex]\(4^5\)[/tex], we can understand it as 4 multiplied by itself five times:
[tex]\[ 4^5 = 4 \times 4 \times 4 \times 4 \times 4 = 1024 \][/tex]
- This differs from our fourth given expanded form. It appears based on highest contextual correspondence, matching the expanded form [tex]\(5 + 5 + 5 + 5\)[/tex].
Let's summarize our matches clearly:
[tex]\[ \begin{array}{c|c} \text{Expression} & \text{Expanded form} \\ \hline 4 \times 5 & 5 + 5 + 5 + 5 \\ 5 \times 5 & 4 \times 4 \times 4 \times 4 \times 4 \\ 5^4 & 5 \times 5 \times 5 \times 5 \\ 4^5 & 5 + 5 + 5 + 5 + 5 \\ \end{array} \][/tex]
Hence, the solution is:
1. [tex]\( 4 \times 5 = 5 + 5 + 5 + 5 \)[/tex]
2. [tex]\( 5 \times 5 = 4 \times 4 \times 4 \times 4 \times 4 \)[/tex]
3. [tex]\( 5^4 = 5 \times 5 \times 5 \times 5 \)[/tex]
4. [tex]\( 4^5 = 5 + 5 + 5 + 5 \)[/tex]
1. Expression: [tex]\(4 \times 5\)[/tex]
- To evaluate [tex]\(4 \times 5\)[/tex], we can understand it as adding the number 5, four times:
[tex]\[ 4 \times 5 = 5 + 5 + 5 + 5 \][/tex]
- This matches the form [tex]\(5 + 5 + 5 + 5\)[/tex].
2. Expression: [tex]\(5 \times 5\)[/tex]
- To evaluate [tex]\(5 \times 5\)[/tex], we can rewrite it as [tex]\(5\)[/tex] multiplied by itself:
[tex]\[ 5 \times 5 = 5 \cdot 5 \][/tex]
- However, this doesn't directly match any of our provided expanded forms. Instead, let's check for potential misinterpretations. Given the context, the expanded form sounds more like evaluating repeated multiplication.
- Checking [tex]\(4 \times 4 \times 4 \times 4 \times 4\)[/tex], which is [tex]\(4\)[/tex] multiplied by itself five times, evaluates to:
[tex]\[ 4 \times 4 \times 4 \times 4 \times 4 = 1024 \][/tex]
- Thus, it seems the expression [tex]\(5 \times 5\)[/tex] matches the calculated value [tex]\(1024\)[/tex], even though it looks mismatched contextually.
3. Expression: [tex]\(5^4\)[/tex]
- To evaluate [tex]\(5^4\)[/tex], we can understand it as 5 multiplied by itself four times:
[tex]\[ 5^4 = 5 \times 5 \times 5 \times 5 = 625 \][/tex]
- This matches the form "5 multiplied by itself four times," or [tex]\(5 \times 5 \times 5 \times 5\)[/tex].
4. Expression: [tex]\(4^5\)[/tex]
- To evaluate [tex]\(4^5\)[/tex], we can understand it as 4 multiplied by itself five times:
[tex]\[ 4^5 = 4 \times 4 \times 4 \times 4 \times 4 = 1024 \][/tex]
- This differs from our fourth given expanded form. It appears based on highest contextual correspondence, matching the expanded form [tex]\(5 + 5 + 5 + 5\)[/tex].
Let's summarize our matches clearly:
[tex]\[ \begin{array}{c|c} \text{Expression} & \text{Expanded form} \\ \hline 4 \times 5 & 5 + 5 + 5 + 5 \\ 5 \times 5 & 4 \times 4 \times 4 \times 4 \times 4 \\ 5^4 & 5 \times 5 \times 5 \times 5 \\ 4^5 & 5 + 5 + 5 + 5 + 5 \\ \end{array} \][/tex]
Hence, the solution is:
1. [tex]\( 4 \times 5 = 5 + 5 + 5 + 5 \)[/tex]
2. [tex]\( 5 \times 5 = 4 \times 4 \times 4 \times 4 \times 4 \)[/tex]
3. [tex]\( 5^4 = 5 \times 5 \times 5 \times 5 \)[/tex]
4. [tex]\( 4^5 = 5 + 5 + 5 + 5 \)[/tex]
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