Question

Which of the following expressions are equivalent to 3-8/3-4 select all that apply

Answer 1

You have the following expression:

(3⁻⁸)/(3⁻⁴)

in order to simplify the previous expression, consider that the quotient in between two number with the same base is given by:

`(x^a)/(x^b)=x^(a-b)`

Hence, for the given expression, you have:

`(3^(-8))/(3^(-4))=3^(-8-(-4))=3^(-8+4)=3^(-4)`

moreover, consider that any number with a negative exponent can be written as 1 over the same number with positive exponent, then, you have:

`3^(-4)=(1)/(3^(4))`

Hence, the simplified expression is 1/3⁴, or 3⁻⁴