Question
Select the equivalent expression.
\[3^{-5}=?\]
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[\dfrac{1}{3^5}\]
A
\[\dfrac{1}{3^5}\]
(Choice B)
\[-3^5\]
B
\[-3^5\]
(Choice C)
\[(-3)^5\]
C
\[(-3)^5\]
\[3^{-5}=?\]
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[\dfrac{1}{3^5}\]
A
\[\dfrac{1}{3^5}\]
(Choice B)
\[-3^5\]
B
\[-3^5\]
(Choice C)
\[(-3)^5\]
C
\[(-3)^5\]
Answers
Answered by
GPT-4o mini
To find the equivalent expression for \(3^{-5}\), we can use the rule of exponents that states \(a^{-n} = \frac{1}{a^n}\).
Applying that rule:
\[
3^{-5} = \frac{1}{3^5}
\]
Now, let's compare this with the given choices:
- (Choice A) \(\dfrac{1}{3^5}\)
- (Choice B) \(-3^5\)
- (Choice C) \((-3)^5\)
The only choice that matches our calculation \(3^{-5} = \dfrac{1}{3^5}\) is:
**(Choice A) \(\dfrac{1}{3^5}\)**.
So, the equivalent expression is:
\(\dfrac{1}{3^5}\).
Applying that rule:
\[
3^{-5} = \frac{1}{3^5}
\]
Now, let's compare this with the given choices:
- (Choice A) \(\dfrac{1}{3^5}\)
- (Choice B) \(-3^5\)
- (Choice C) \((-3)^5\)
The only choice that matches our calculation \(3^{-5} = \dfrac{1}{3^5}\) is:
**(Choice A) \(\dfrac{1}{3^5}\)**.
So, the equivalent expression is:
\(\dfrac{1}{3^5}\).
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