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, let's evaluate each expression step-by-step.
First, consider the expression [tex]\( 5\left(\frac{1}{5^3}\right) \)[/tex]:
1. Calculate [tex]\( 5^3 \)[/tex]:
[tex]\[ 5^3 = 5 \times 5 \times 5 = 125 \][/tex]
2. Take the reciprocal of [tex]\( 5^3 \)[/tex]:
[tex]\[ \frac{1}{5^3} = \frac{1}{125} \][/tex]
3. Multiply 5 by [tex]\( \frac{1}{125} \)[/tex]:
[tex]\[ 5 \left(\frac{1}{125}\right) = \frac{5}{125} = \frac{1}{25} \][/tex]
Now, let's evaluate the second expression [tex]\( 5 \left(5^3\right) \)[/tex]:
1. Calculate [tex]\( 5^3 \)[/tex]:
[tex]\[ 5^3 = 5 \times 5 \times 5 = 125 \][/tex]
2. Multiply 5 by 125:
[tex]\[ 5 \times 125 = 625 \][/tex]
Comparing the two results:
- The first expression [tex]\( 5\left(\frac{1}{5^3}\right) \)[/tex] equals [tex]\( \frac{1}{25} \)[/tex].
- The second expression [tex]\( 5\left(5^3\right) \)[/tex] equals 625.
Therefore, the two expressions are not equal. The correct answer is:
No; The first expression is equal to [tex]\(\frac{1}{25}\)[/tex] and the second expression is equal to 625.
First, consider the expression [tex]\( 5\left(\frac{1}{5^3}\right) \)[/tex]:
1. Calculate [tex]\( 5^3 \)[/tex]:
[tex]\[ 5^3 = 5 \times 5 \times 5 = 125 \][/tex]
2. Take the reciprocal of [tex]\( 5^3 \)[/tex]:
[tex]\[ \frac{1}{5^3} = \frac{1}{125} \][/tex]
3. Multiply 5 by [tex]\( \frac{1}{125} \)[/tex]:
[tex]\[ 5 \left(\frac{1}{125}\right) = \frac{5}{125} = \frac{1}{25} \][/tex]
Now, let's evaluate the second expression [tex]\( 5 \left(5^3\right) \)[/tex]:
1. Calculate [tex]\( 5^3 \)[/tex]:
[tex]\[ 5^3 = 5 \times 5 \times 5 = 125 \][/tex]
2. Multiply 5 by 125:
[tex]\[ 5 \times 125 = 625 \][/tex]
Comparing the two results:
- The first expression [tex]\( 5\left(\frac{1}{5^3}\right) \)[/tex] equals [tex]\( \frac{1}{25} \)[/tex].
- The second expression [tex]\( 5\left(5^3\right) \)[/tex] equals 625.
Therefore, the two expressions are not equal. 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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