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:

$\frac{x^a}{x^b}=x^{a-b}$

Hence, for the given expression, you have:

$\frac{3^{-8}}{3^{-4}}=3^{-8-(-4)}=3^{-8+4}=3^{-4}$

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

$3^{-4}=\frac{1}{3^{4}}$

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