Question

simplify.
$u^{-9} \cdot u^{-5}$
write your answer with a positive exponent only.

Explanation:

Step1: Apply exponent rule for multiplication

When multiplying two terms with the same base, we add the exponents. The rule is \(a^m \cdot a^n = a^{m + n}\). For \(u^{-9} \cdot u^{-5}\), the base \(a = u\), \(m=-9\), and \(n = -5\). So we add the exponents: \(-9+(-5)=-14\). Thus, \(u^{-9} \cdot u^{-5}=u^{-14}\).

Step2: Convert to positive exponent

The rule for negative exponents is \(a^{-n}=\frac{1}{a^n}\). So for \(u^{-14}\), we can rewrite it as \(\frac{1}{u^{14}}\).

Answer:

\(\frac{1}{u^{14}}\)