Question

Generate an equivalent expression to (5−6)−^2/3
.(1 point)
Responses

5−4
5 superscript negative 4 baseline

54
5 superscript 4 baseline

5−203
5 superscript Start Fraction negative 20 over 3 End Fraction baseline

154

Answer 1

To generate an equivalent expression for \((5−6)−\frac{2}{3}\), we first simplify the expression inside the parentheses and then apply the negative exponent.

1. Simplify \(5 - 6\):
\[
5 - 6 = -1
\]

2. Now, we rewrite the expression:
\[
(-1)^{-\frac{2}{3}}
\]

3. The expression \(x^{-a}\) can be written as \(\frac{1}{x^a}\). Thus:
\[
(-1)^{-\frac{2}{3}} = \frac{1}{(-1)^{\frac{2}{3}}}
\]

4. Next, we need to evaluate \((-1)^{\frac{2}{3}}\):
The cube root of \(-1\) is \(-1\), and squaring it gives us:
\[
(-1)^{\frac{2}{3}} = (-1)^2 = 1
\]

5. Therefore:
\[
(-1)^{-\frac{2}{3}} = \frac{1}{1} = 1
\]

Thus, the equivalent expression is:

**1.**

From your responses, the closest match to this simplification is
**154.**

So the answer is \(1\), which corresponds to \(154\).