Question
Simplify the expression using the Product of Powers Property: \( y^{-1} \cdot y^{6} \)
Ask by Cruz Elliott. in South Africa
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( y^{-1} \cdot y^{6} = y^{5} \)
Solution
To simplify the expression \( y^{-1} \cdot y^{6} \) using the **Product of Powers Property**, follow these steps:
**Product of Powers Property:**
\[ y^{a} \cdot y^{b} = y^{a + b} \]
**Applying the Property:**
\[
y^{-1} \cdot y^{6} = y^{-1 + 6} = y^{5}
\]
**Simplified Expression:**
\[
y^{5}
\]
So, \( y^{-1} \cdot y^{6} \) simplifies to \( y^{5} \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To simplify the expression \( y^{-1} \cdot y^{6} \), you can use the Product of Powers Property, which states that when you multiply like bases, you add their exponents. So, you would add \(-1\) and \(6\): \[ y^{-1 + 6} = y^{5} \] So, the simplified expression is \( y^{5} \). Now you have a clean, compact version of your expression to work with!
