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Answer :
Let's evaluate both expressions step by step to determine if they are equal:
1. First Expression: [tex]\(5\left(\frac{1}{5^3}\right)\)[/tex]
- First, calculate [tex]\(5^3\)[/tex]:
[tex]\[
5^3 = 5 \times 5 \times 5 = 125
\][/tex]
- Then, find [tex]\(\frac{1}{5^3}\)[/tex]:
[tex]\[
\frac{1}{5^3} = \frac{1}{125}
\][/tex]
- Now multiply by 5:
[tex]\[
5 \times \frac{1}{125} = \frac{5}{125} = \frac{1}{25}
\][/tex]
The value of the first expression is [tex]\(\frac{1}{25}\)[/tex].
2. Second Expression: [tex]\(5\left(5^3\right)\)[/tex]
- Using the same calculation for [tex]\(5^3\)[/tex] from above:
[tex]\[
5^3 = 125
\][/tex]
- Then multiply by 5:
[tex]\[
5 \times 125 = 625
\][/tex]
The value of the second expression is 625.
3. Comparison
- The first expression equals [tex]\(\frac{1}{25}\)[/tex].
- The second expression equals 625.
Since [tex]\(\frac{1}{25}\)[/tex] is not equal to 625, the two expressions are not equal. So, the correct answer is:
No; The first expression is equal to [tex]\(\frac{1}{25}\)[/tex] and the second expression is equal to 625.
1. First Expression: [tex]\(5\left(\frac{1}{5^3}\right)\)[/tex]
- First, calculate [tex]\(5^3\)[/tex]:
[tex]\[
5^3 = 5 \times 5 \times 5 = 125
\][/tex]
- Then, find [tex]\(\frac{1}{5^3}\)[/tex]:
[tex]\[
\frac{1}{5^3} = \frac{1}{125}
\][/tex]
- Now multiply by 5:
[tex]\[
5 \times \frac{1}{125} = \frac{5}{125} = \frac{1}{25}
\][/tex]
The value of the first expression is [tex]\(\frac{1}{25}\)[/tex].
2. Second Expression: [tex]\(5\left(5^3\right)\)[/tex]
- Using the same calculation for [tex]\(5^3\)[/tex] from above:
[tex]\[
5^3 = 125
\][/tex]
- Then multiply by 5:
[tex]\[
5 \times 125 = 625
\][/tex]
The value of the second expression is 625.
3. Comparison
- The first expression equals [tex]\(\frac{1}{25}\)[/tex].
- The second expression equals 625.
Since [tex]\(\frac{1}{25}\)[/tex] is not equal to 625, the two expressions are not equal. So, the correct answer is:
No; The first expression is equal to [tex]\(\frac{1}{25}\)[/tex] and the second expression is equal to 625.
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