Question
Generate an equivalent expression to (5^−6)^−2/3
.(1 point)
Responses
5^4
5 superscript 4 baseline
5^−4
5 superscript negative 4 baseline
5^−20/3
5 superscript Start Fraction negative 20 over 3 End Fraction baseline
1/5^4
Start Fraction 1 over 5 superscript 4 baseline End Fraction
.(1 point)
Responses
5^4
5 superscript 4 baseline
5^−4
5 superscript negative 4 baseline
5^−20/3
5 superscript Start Fraction negative 20 over 3 End Fraction baseline
1/5^4
Start Fraction 1 over 5 superscript 4 baseline End Fraction
Answers
Answer
thats wrong
Answer
OH IM DUMB IM SORRY BOT YOURE RIGHT-
Answered by
GPT-4o mini
To simplify the expression \((5^{-6})^{-2/3}\), we can start by applying the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\).
1. Applying this property:
\[
(5^{-6})^{-2/3} = 5^{-6 \cdot (-2/3)}
\]
2. Now, calculate \(-6 \cdot (-2/3)\):
\[
-6 \cdot (-2/3) = 12/3 = 4
\]
3. Therefore, we have:
\[
(5^{-6})^{-2/3} = 5^4
\]
Thus, the equivalent expression is \(5^4\).
**Final Response:**
5^4
1. Applying this property:
\[
(5^{-6})^{-2/3} = 5^{-6 \cdot (-2/3)}
\]
2. Now, calculate \(-6 \cdot (-2/3)\):
\[
-6 \cdot (-2/3) = 12/3 = 4
\]
3. Therefore, we have:
\[
(5^{-6})^{-2/3} = 5^4
\]
Thus, the equivalent expression is \(5^4\).
**Final Response:**
5^4
Answered by
GPT-4o mini
Let’s carefully work through the expression step-by-step again:
Given the expression \((5^{-6})^{-2/3}\), we will simplify this using the properties of exponents.
1. **Apply the Power of a Power Rule:**
\[
(a^m)^n = a^{m \cdot n}
\]
So,
\[
(5^{-6})^{-2/3} = 5^{-6 \cdot (-2/3)}
\]
2. **Calculate the exponent:**
\[
-6 \cdot -\frac{2}{3} = \frac{12}{3} = 4
\]
3. **Substitute back:**
\[
(5^{-6})^{-2/3} = 5^4
\]
Thus, the simplified expression is indeed \(5^4\).
The answer choices were:
- \(5^4\)
- \(5^{-4}\)
- \(5^{-20/3}\)
- \(\frac{1}{5^4}\)
Since \(5^4\) matches one of the options, that is the correct expression.
If there's an error in interpreting the question or the answer options, please let me know!
Given the expression \((5^{-6})^{-2/3}\), we will simplify this using the properties of exponents.
1. **Apply the Power of a Power Rule:**
\[
(a^m)^n = a^{m \cdot n}
\]
So,
\[
(5^{-6})^{-2/3} = 5^{-6 \cdot (-2/3)}
\]
2. **Calculate the exponent:**
\[
-6 \cdot -\frac{2}{3} = \frac{12}{3} = 4
\]
3. **Substitute back:**
\[
(5^{-6})^{-2/3} = 5^4
\]
Thus, the simplified expression is indeed \(5^4\).
The answer choices were:
- \(5^4\)
- \(5^{-4}\)
- \(5^{-20/3}\)
- \(\frac{1}{5^4}\)
Since \(5^4\) matches one of the options, that is the correct expression.
If there's an error in interpreting the question or the answer options, please let me know!
Answered by
GPT-4o mini
No need to apologize! It's completely normal to have questions and double-check things, especially when working with math. I'm glad we could clarify the expression together. If you have any more questions or if there's anything else you'd like to discuss, feel free to ask!