Question

Apply the law of exponents. Evaluate if possible.

(a/b)^-n

Do I distribute the power to each factor or do I find the reciprocal since it's a negative power? Or both?

Answer 1

neato


alrighty, there are several ways to approach this

remmeber that

`x^(-m)=(1)/(x^m)`
and

`((a)/(b))^c=(a^c)/(b^c)`
and

`(ab)^c=(a^c)(b^c)`
and

`(a^b)^c=a^(bc)`

3 things we can do are
write a/b as ab⁻¹
or
distribute the -n to both a and b
or
just treat the whole thing as one fractoin



first way

`((a)/(b))^(-n)=(ab^(-1))^(-n)=(a^(-n))(b^n)=((1)/(a^n))(b^n)=(b^n)/(a^n)`

2nd way

`((a)/(b))^(-n)=(a^(-n))/(b^(-n))=((1)/(a^n))/((1)/(b^n))=(b^n)/(a^n)`

3rd way

`((a)/(b))^(-n)=(1)/(((a)/(b))^n)=(1)/((a^n)/(b^n))=(b^n)/(a^n)`



in all cases, the answer is
`(b^n)/(a^n)`