Question
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Answer
La expresión se simplifica a \(9^{21}\).
Solution
Calculate or simplify the expression \( 9^{4} \cdot 9^{3} \cdot(9^{2})^{7} \).
Calculate the value by following steps:
- step0: Calculate:
\(9^{4}\times 9^{3}\left(9^{2}\right)^{7}\)
- step1: Multiply the exponents:
\(9^{4}\times 9^{3}\times 9^{2\times 7}\)
- step2: Multiply the numbers:
\(9^{4}\times 9^{3}\times 9^{14}\)
- step3: Multiply the terms:
\(9^{4+3+14}\)
- step4: Add the numbers:
\(9^{21}\)
La expresión \(9^{4} \cdot 9^{3} \cdot (9^{2})^{7}\) se simplifica a \(9^{21}\) o aproximadamente \(1.09419 \times 10^{20}\).
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Simplify this solution The Deep Dive
To simplify \( 9^{4} \cdot 9^{3} \cdot \left(9^{2}\right)^{7} \), we can first apply the laws of exponents. For the first two terms, we use the property \( a^m \cdot a^n = a^{m+n} \): \[ 9^{4} \cdot 9^{3} = 9^{4+3} = 9^{7} \] Next, we simplify \( \left(9^{2}\right)^{7} \) using the power of a power property \( (a^m)^n = a^{m \cdot n} \): \[ \left(9^{2}\right)^{7} = 9^{2 \cdot 7} = 9^{14} \] Now, we can combine \( 9^{7} \) and \( 9^{14} \): \[ 9^{7} \cdot 9^{14} = 9^{7+14} = 9^{21} \] Thus, the simplified expression is: \[ 9^{21} \]
