True or False?

Question

The work below shows the correct process for simplifying the expression.

(34)−3=3−34−3=3343=27256
(
3
4
)
−
3
=
3
−
3
4
−
3
=
3
3
4
3
=
27
256
(1 point)
Responses

True
True

False

Answer 1

False

The shown process for simplifying the expression \((\frac{3}{4})^{-3}\) is incorrect. The correct approach is to rewrite the negative exponent as follows:

\[ (\frac{3}{4})^{-3} = (\frac{4}{3})^{3} = \frac{4^3}{3^3} = \frac{64}{27} \]

Thus, the final answer is \(\frac{64}{27}\), not \(\frac{27}{256}\).