True or False? The work below shows the correct process for simplifying the expression. (23)−3=2−33−3=3323=278(23)−3=2−33−3=3323=278 (1 point) Responses True True False False

Answer 1

False.

Let's analyze the expression step by step. The expression \((2^3)^{-3}\) should be simplified as follows:

1. Use the power of a power property: \((a^m)^n = a^{m \cdot n}\). \[ (2^3)^{-3} = 2^{3 \cdot (-3)} = 2^{-9} \]

2. Rewrite \(2^{-9}\) using the negative exponent rule: \(a^{-n} = \frac{1}{a^n}\). \[ 2^{-9} = \frac{1}{2^9} \]

3. Calculate \(2^9 = 512\). \[ 2^{-9} = \frac{1}{512} \]

Therefore, the correct simplified form is \(2^{-9} = \frac{1}{512}\), and the work shown in the question is incorrect. Thus, the answer is False.