Question

simplify.
\\(\frac{b^{-3}}{b^{7}}\\)
write your answer with a positive exponent only.

Explanation:

Step1: Use exponent rule for division

When dividing with the same base, subtract the exponents: $ \frac{b^m}{b^n} = b^{m - n} $. Here, $ m = -3 $ and $ n = 7 $, so we have $ b^{-3 - 7} $.
$ b^{-3 - 7} = b^{-10} $

Step2: Convert negative exponent to positive

Use the rule $ b^{-n} = \frac{1}{b^n} $, so $ b^{-10} = \frac{1}{b^{10}} $.

Answer:

$\frac{1}{b^{10}}$