Answer:
1) 4 s^(-3) t^(-4) / (8 s^6 t^8) = s^(-9) t^(-12) / 2
2) 7 a^(-3) b^9 / [2 a^2 b^(-5)] = 7 a^(-5) b^14 / 2
Step-by-step explanation:
1) 4 s^(-3) t^(-4) / (8 s^6 t^8)
Dividind the numerator and denominator by 4:
[4 s^(-3) t^(-4)]/4 / (8 s^6 t^8)/4 = s^(-3) t^(-4) / (2 s^6 t^8)
Using quotient rule: a^m/a^n=a^(m-n):
s^(-3) t^(-4) / (2 s^6 t^8) = s^(-3-6) t^(-4-8) / 2 = s^(-9) t^(-12) / 2
2) 7 a^(-3) b^9 / [2 a^2 b^(-5)]
Using quotient rule: a^m/a^n=a^(m-n):
7 a^(-3) b^9 / [2 a^2 b^(-5)] = 7 a^(-3-2) b^(9-(-5)) / 2
7 a^(-3) b^9 / [2 a^2 b^(-5)] = 7 a^(-5) b^(9+5) / 2
7 a^(-3) b^9 / [2 a^2 b^(-5)] = 7 a^(-5) b^14 / 2
