Questions: Simplify. w^3 cdot w^-8 Write your answer with a positive exponent only.

Solution Steps

When multiplying two expressions with the same base, we add their exponents. That is: \[ w^{a} \cdot w^{b} = w^{a + b} \] Here, \( a = 3 \) and \( b = -8 \). So: \[ w^{3} \cdot w^{-8} = w^{3 + (-8)} = w^{-5} \]

To express \( w^{-5} \) with a positive exponent, we use the rule: \[ w^{-n} = \frac{1}{w^{n}} \] Thus: \[ w^{-5} = \frac{1}{w^{5}} \]

Final Answer