For this case we must simplify the following expression:
[tex](4a^{ - 6} * b ^ 2)^{ - 3}[/tex]
By definition of power properties we have:[tex]a ^ {-1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
Then, rewriting the expression:
[tex](\frac {4} {a ^ 6} * b ^ 2) ^ {- 3} =\\\frac {1} {(\frac {4} {a ^ 6} * b ^ 2)^3} =\\\frac {1} {(\frac {4b ^ 2} {a ^ 6})^3} =[/tex]
By definition we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
[tex]\frac {1} {\frac {64b ^ 6} {a^{18}}}\\\frac {a^{18}} {64b ^ 6}[/tex]
Answer:
[tex]\frac {a^{18}} {64b ^ 6}[/tex]
