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.