For this case we must simplify the following expression:
[tex]\frac {(5 ^ 3) ^ 9} {5 ^ {12}}[/tex]
By definition of power properties we have:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
So, we can rewrite the expression as:
[tex]\frac {5 ^ {3 * 9}} {5 ^ {12}} =\\\frac {5 ^ {27}} {5 ^ {12}} =[/tex]
By definition of division of powers of the same base we have:
[tex]\frac {a ^ m} {a ^ n} = a ^ {m-n}[/tex]
So:
[tex]5^{ 27-12} = 5 ^ {15}[/tex]
Answer:
[tex]5 ^ {15}[/tex]
