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