Question
Simplify the given expression. \( k^{8}\left(k^{9}\right)^{9}= \) Question Help: \( \square \) Message instructor Submit Question
Ask by Ortiz Chandler. in the United States
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( k^{89} \)
Solution
To simplify the expression \( k^{8}\left(k^{9}\right)^{9} \), follow these steps:
1. **Simplify the Exponentiation:**
Apply the power of a power rule, which states \((a^m)^n = a^{m \times n}\).
\[
\left(k^{9}\right)^{9} = k^{9 \times 9} = k^{81}
\]
2. **Multiply the Terms with the Same Base:**
When multiplying terms with the same base, add their exponents.
\[
k^{8} \times k^{81} = k^{8 + 81} = k^{89}
\]
**Final Simplified Expression:**
\[
k^{89}
\]
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Simplify this solution Mind Expander
To simplify the expression \( k^{8}\left(k^{9}\right)^{9} \), we first apply the power of a power rule, which states that \( (a^m)^n = a^{m \cdot n} \). So, we have: \[ \left(k^{9}\right)^{9} = k^{9 \cdot 9} = k^{81}. \] Now, we can combine the exponents since they have the same base \( k \): \[ k^{8} \cdot k^{81} = k^{8 + 81} = k^{89}. \] Thus, the simplified expression is \( k^{89} \).
