Answer:
\(\dfrac{x^{12}}{64}\)
Step-by-step explanation:
Given: \((4x^{-4})^{-3}\)
We need to simplify it
Here we have exponent of exponent
Exponent law:
\((a^m)^n=a^{mn}\)
\(a^{-m}=\dfrac{1}{a^m}\)
First we distribute the exponent -3 with each term inside the bracket.
\(\Rightarrow (4x^{-4})^{-3}\)
\(\Rightarrow 4^{-3}(x^{-4})^{-3}\)
\(\Rightarrow 64^{-1}x^{-4\cdot -3}\)
\(\Rightarrow 64^{-1}x^{12}\)
\(\Rightarrow \dfrac{x^{12}}{64}\)
Hence, The simplified expression is \(\Rightarrow \dfrac{x^{12}}{64}\)
