Which of the following would represent the correct process for simplifying the expression below?

Question

3−23−3=
3
−
2
3
−
3
=
(1 point)
Responses

3−23−3=3((−2)−3)=3−5=135=1243
3
−
2
3
−
3
=
3
(
(
−
2
)
−
3
)
=
3
−
5
=
1
3
5
=
1
243
the fraction with numerator 3 to the negative 2 power and denominator 3 to the negative 3 power is equal to 3 raised to the open paren negative 2 minus 3 close paren power is equal to 3 to the negative 5 power is equal to the fraction with numerator 1 and denominator 3 to the 5th power is equal to 1 over 243

3−23−3=3(−2)⋅(−3)=36=729
3
−
2
3
−
3
=
3
(
−
2
)
⋅
(
−
3
)
=
3
6
=
729
the fraction with numerator 3 to the negative 2 power and denominator 3 to the negative 3 power is equal to 3 raised to the negative 2 times negative 3 power is equal to 3 to the 6th power is equal to 729

3−23−3=3(−2)−(−3)=31=3

Answer 1

To simplify the expression \( \frac{3^{-2}}{3^{-3}} \), we can use the properties of exponents. The general rule is that:

\[ \frac{a^m}{a^n} = a^{m-n} \]

Applying this rule to your expression:

\[ \frac{3^{-2}}{3^{-3}} = 3^{-2 - (-3)} = 3^{-2 + 3} = 3^{1} = 3 \]

None of the responses presented correctly simplify the expression according to the proper exponent rules. The simplest and correct process is:

1. Rewrite \( \frac{3^{-2}}{3^{-3}} \).
2. Apply the exponent rule: \( 3^{-2 - (-3)} = 3^{1} = 3 \).

However, here’s a summary of the incorrect responses:

• The first response suggests \( 3^{-2} - 3 = 3^{(-2) - 3} \) which is incorrect.
• The second response incorrectly states that multiplication of exponents gives a power of 6.
• The last response mixes subtraction and evaluates incorrectly.

Therefore, the correct answer simplifies directly to \( 3 \), but it seems the provided responses were not accurate in their calculations or interpretations of exponent rules.