Question
Question 15
Use Efficient Methods Without evaluating, order 5−7
, 54
, and 50
from least to greatest. Explain your reasoning. Choose the correct answer and explanation.
Multiple choice question.
cross out
A)
54, 50, 5−7
; The expression 54
is greater than 1, 50
equals 1, and when written with a positive exponent, 5−7
is 157
and is less than 1.
cross out
B)
5−7, 50,54
; The expression 5−7
has a negative value and is less than 1, 50
equals 0, and 54
is greater than 1.
cross out
C)
50,5−7, 54
; The expression 50
equals 0, written with a positive exponent, 5−7
is 157
and is less than 1, and 54
is greater than 1.
cross out
D)
5−7, 50,54
; Written with a positive exponent, 5−7
is 157
and is less than 1, 50
equals 1, and 54
is greater than 1.
Use Efficient Methods Without evaluating, order 5−7
, 54
, and 50
from least to greatest. Explain your reasoning. Choose the correct answer and explanation.
Multiple choice question.
cross out
A)
54, 50, 5−7
; The expression 54
is greater than 1, 50
equals 1, and when written with a positive exponent, 5−7
is 157
and is less than 1.
cross out
B)
5−7, 50,54
; The expression 5−7
has a negative value and is less than 1, 50
equals 0, and 54
is greater than 1.
cross out
C)
50,5−7, 54
; The expression 50
equals 0, written with a positive exponent, 5−7
is 157
and is less than 1, and 54
is greater than 1.
cross out
D)
5−7, 50,54
; Written with a positive exponent, 5−7
is 157
and is less than 1, 50
equals 1, and 54
is greater than 1.
Answers
GPT-4o mini
To compare \( 5^{-7} \), \( 50 \), and \( 54 \) without evaluating them directly, let's analyze each expression.
1. **Evaluate \( 5^{-7} \):**
- The expression \( 5^{-7} \) is equivalent to \( \frac{1}{5^7} \). Since \( 5^7 \) is a positive number greater than 1, \( \frac{1}{5^7} \) is a positive number less than 1.
2. **Evaluate \( 50 \):**
- The expression \( 50 \) is equal to 1 because \( 5^0 = 1 \).
3. **Evaluate \( 54 \):**
- The expression \( 54 \) is greater than 1 since \( 5^4 = 625 \) which is much greater than 1.
Now, we can order these three values:
- \( 5^{-7} < 1\) (since it is less than 1),
- \( 50 = 1 \),
- \( 54 > 1 \).
So, the correct order from least to greatest is:
- \( 5^{-7} < 50 < 54 \).
Now let’s look at the options provided:
**A)** 54, 50, 5−7 – Incorrect
**B)** 5−7, 50, 54 – Correct based on our analysis, but misidentified as negative in the explanation.
**C)** 50, 5−7, 54 – Incorrect
**D)** 5−7, 50, 54 – Correct based on our analysis and contains the right reasoning as well.
The best answer considering the reasoning offered, is:
**D)** 5−7, 50, 54.
1. **Evaluate \( 5^{-7} \):**
- The expression \( 5^{-7} \) is equivalent to \( \frac{1}{5^7} \). Since \( 5^7 \) is a positive number greater than 1, \( \frac{1}{5^7} \) is a positive number less than 1.
2. **Evaluate \( 50 \):**
- The expression \( 50 \) is equal to 1 because \( 5^0 = 1 \).
3. **Evaluate \( 54 \):**
- The expression \( 54 \) is greater than 1 since \( 5^4 = 625 \) which is much greater than 1.
Now, we can order these three values:
- \( 5^{-7} < 1\) (since it is less than 1),
- \( 50 = 1 \),
- \( 54 > 1 \).
So, the correct order from least to greatest is:
- \( 5^{-7} < 50 < 54 \).
Now let’s look at the options provided:
**A)** 54, 50, 5−7 – Incorrect
**B)** 5−7, 50, 54 – Correct based on our analysis, but misidentified as negative in the explanation.
**C)** 50, 5−7, 54 – Incorrect
**D)** 5−7, 50, 54 – Correct based on our analysis and contains the right reasoning as well.
The best answer considering the reasoning offered, is:
**D)** 5−7, 50, 54.