For this case, we must find an expression equivalent to:
[tex]\frac {28p ^ 9 * q ^ {- 5}} {12p ^ {- 6} * q ^ 7}[/tex]
By definition of power properties we have:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
Rewriting the previous expression we have:
We take into account that:
[tex]\frac {28} {12} = \frac {14} {6} = \frac {7} {3}[/tex]
So:
[tex]\frac {7p ^ 9 * p ^ 6} {3q ^ 5 q ^ 7} =[/tex]
According to one of the properties of powers of the same base, we must put the same base and add the exponents:
[tex]\frac {7p ^ {9+6}} {3q ^ {5+7}} =\\\frac {7p ^ {15}} {3q ^ {12}}[/tex]
Answer:
[tex]\frac {7p ^ {15}} {3q ^ {12}}[/tex]
Option B
