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

3−23−3=
(1 point)
Responses

3−23−3=3((−2)−3)=3−5=135=1243
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
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

1 answer

To simplify the expression \( \frac{3^{-2}}{3^{-3}} \), we can use the property of exponents that states

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

Apply this to the expression:

  1. Rewrite the expression with the property: \[ \frac{3^{-2}}{3^{-3}} = 3^{-2-(-3)} = 3^{-2 + 3} = 3^{1}. \]

  2. This simplifies to: \[ 3^{1} = 3. \]

Now looking at the provided responses, the third response which simplifies to \(3^{1}\) is correct:

\(3^{-2} \div 3^{-3} = 3^{(-2) - (-3)} = 3^1 = 3\).

Therefore, the correct response is:

3−23−3=3(−2)−(−3)=31=3.