Question

Use Quotient rule and simplify

Show work please!

1. 4s^3t^-4/8s^6t^8


4. 7a^-3b^9/2a^2b^-5

Answer 1

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

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