Question

simplify.
$u^2 \cdot u \cdot u^{-5}$
write your answer with a positive exponent only.

Explanation:

Step1: Recall exponent rule \(a^m \cdot a^n = a^{m + n}\)

Here, \(u = u^1\), so \(u^2 \cdot u \cdot u^{-5}=u^{2 + 1+(-5)}\)

Step2: Calculate the exponent

\(2 + 1+(-5)=2 + 1 - 5=-2\), so we have \(u^{-2}\)

Step3: Use rule \(a^{-n}=\frac{1}{a^n}\)

\(u^{-2}=\frac{1}{u^2}\)

Answer:

\(\frac{1}{u^{2}}\)