Question

simplify.
$w^{-4} \cdot w^{7}$
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 \(a^m \cdot a^n = a^{m + n}\). Here, the base is \(w\), \(m=-4\) and \(n = 7\). So we have \(w^{-4}\cdot w^{7}=w^{-4 + 7}\).

Step2: Calculate the exponent

Simplify the exponent: \(-4+7 = 3\). So the expression becomes \(w^{3}\).

Answer:

\(w^{3}\)