Subjects algebra

Multiply Divide Powers

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1. The problem asks us to simplify the expression $$z^{-11} \cdot z^{-15}$$ and rewrite it in the form $$z^n$$. 2. Recall the rule for multiplying powers with the same base: $$a^m \cdot a^n = a^{m+n}$$. 3. Apply this rule to the expression: $$z^{-11} \cdot z^{-15} = z^{-11 + (-15)} = z^{-26}$$. 4. The simplified expression is $$z^{-26}$$. 5. This is already in the form $$z^n$$ where $$n = -26$$. Final answer: $$z^{-26}$$.