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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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