Thank you for visiting Is tex 5 left frac 1 5 3 right 5 left 5 3 right tex Explain A Yes both expressions are equal to 625 B. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To determine whether the expressions [tex]\(5\left(\frac{1}{5^3}\right)\)[/tex] and [tex]\(5\left(5^3\right)\)[/tex] are equal, we need to evaluate each expression separately.
1. First Expression: [tex]\(5\left(\frac{1}{5^3}\right)\)[/tex]
- First, calculate [tex]\(5^3\)[/tex]. [tex]\(5^3\)[/tex] means multiplying 5 by itself three times:
[tex]\[
5 \times 5 \times 5 = 125
\][/tex]
- Now, we need to find [tex]\(\frac{1}{5^3}\)[/tex]:
[tex]\[
\frac{1}{125}
\][/tex]
- Multiply this result by 5:
[tex]\[
5 \times \frac{1}{125} = \frac{5}{125} = \frac{1}{25} = 0.04
\][/tex]
So, the value of the first expression is [tex]\(0.04\)[/tex].
2. Second Expression: [tex]\(5\left(5^3\right)\)[/tex]
- Again, calculate [tex]\(5^3\)[/tex]:
[tex]\[
5^3 = 125
\][/tex]
- Multiply this result by 5:
[tex]\[
5 \times 125 = 625
\][/tex]
So, the value of the second expression is [tex]\(625\)[/tex].
Comparing both results, the first expression evaluates to [tex]\(0.04\)[/tex] and the second expression evaluates to [tex]\(625\)[/tex]. Clearly, these two values are not equal.
Therefore, the correct answer is:
No; The first expression is equal to [tex]\(\frac{1}{25}\)[/tex] (or 0.04) 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]\(5^3\)[/tex] means multiplying 5 by itself three times:
[tex]\[
5 \times 5 \times 5 = 125
\][/tex]
- Now, we need to find [tex]\(\frac{1}{5^3}\)[/tex]:
[tex]\[
\frac{1}{125}
\][/tex]
- Multiply this result by 5:
[tex]\[
5 \times \frac{1}{125} = \frac{5}{125} = \frac{1}{25} = 0.04
\][/tex]
So, the value of the first expression is [tex]\(0.04\)[/tex].
2. Second Expression: [tex]\(5\left(5^3\right)\)[/tex]
- Again, calculate [tex]\(5^3\)[/tex]:
[tex]\[
5^3 = 125
\][/tex]
- Multiply this result by 5:
[tex]\[
5 \times 125 = 625
\][/tex]
So, the value of the second expression is [tex]\(625\)[/tex].
Comparing both results, the first expression evaluates to [tex]\(0.04\)[/tex] and the second expression evaluates to [tex]\(625\)[/tex]. Clearly, these two values are not equal.
Therefore, the correct answer is:
No; The first expression is equal to [tex]\(\frac{1}{25}\)[/tex] (or 0.04) and the second expression is equal to 625.
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