Question
Which of the following was developed to result in 185 when the Properties of Negative Integer Exponents was applied?(1 point)
Responses
8−5
8 superscript negative 5 baseline
5−8
5 superscript negative 8 baseline
85
8 superscript 5 baseline
18−5
Start Fraction 1 over 8 superscript negative 5 baseline End Fraction
Responses
8−5
8 superscript negative 5 baseline
5−8
5 superscript negative 8 baseline
85
8 superscript 5 baseline
18−5
Start Fraction 1 over 8 superscript negative 5 baseline End Fraction
Answers
GPT-4o mini
To determine which option results in 185 when applying the properties of negative integer exponents, we need to evaluate each expression one by one.
1. **\(8^{-5}\)**:
\[
8^{-5} = \frac{1}{8^5}
\]
This does not equal 185.
2. **\(5^{-8}\)**:
\[
5^{-8} = \frac{1}{5^8}
\]
This does not equal 185.
3. **\(8^5\)**:
\[
8^5 = 32768
\]
This does not equal 185.
4. **\(1/8^{-5}\)**:
\[
\frac{1}{8^{-5}} = 8^5
\]
We already calculated \(8^5\) and found it equals 32768, which does not equal 185.
None of the options directly result in 185. Please double-check the calculation or the initial question as none of the given expressions results in 185 according to the properties of negative integer exponents.
1. **\(8^{-5}\)**:
\[
8^{-5} = \frac{1}{8^5}
\]
This does not equal 185.
2. **\(5^{-8}\)**:
\[
5^{-8} = \frac{1}{5^8}
\]
This does not equal 185.
3. **\(8^5\)**:
\[
8^5 = 32768
\]
This does not equal 185.
4. **\(1/8^{-5}\)**:
\[
\frac{1}{8^{-5}} = 8^5
\]
We already calculated \(8^5\) and found it equals 32768, which does not equal 185.
None of the options directly result in 185. Please double-check the calculation or the initial question as none of the given expressions results in 185 according to the properties of negative integer exponents.