Questions: Simplify. w^3 cdot w^-6 Write your answer with a positive exponent only.

Transcript text: Simplify. \[ w^{3} \cdot w^{-6} \] Write your answer with a positive exponent only.

Solution

Step 1: Apply the Product of Powers Rule

The product of powers rule states that when multiplying two exponents with the same base, you add the exponents. Here, the base is \( w \).

\[ w^{3} \cdot w^{-6} = w^{3 + (-6)} \]

Step 2: Simplify the Exponent

Add the exponents from the previous step.

\[ w^{3 + (-6)} = w^{-3} \]

Step 3: Convert to Positive Exponent

To express the answer with a positive exponent, use the property that \( a^{-n} = \frac{1}{a^n} \).

\[ w^{-3} = \frac{1}{w^{3}} \]

\(\boxed{\frac{1}{w^{3}}}\)

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