Pregunta
f. \( \frac{8^{6}}{8^{9}} \times \frac{8^{9}}{8^{4}}= \)
Ask by Erickson Haynes. in South Africa
Feb 25,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( \frac{8^{6}}{8^{9}} \times \frac{8^{9}}{8^{4}} = 8^{(6-9)} \times 8^{(9-4)} = 8^{-3} \times 8^{5} = 8^{(-3+5)} = 8^{2} = 64 \)
Solución
Calculate or simplify the expression \( 8^6/8^9 * 8^9/8^4 \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{\frac{8^{6}}{8^{9}}\times 8^{9}}{8^{4}}\)
- step1: Multiply by \(a^{-n}:\)
\(\frac{8^{6}}{8^{9}}\times 8^{9}\times 8^{-4}\)
- step2: Multiply by \(a^{-n}:\)
\(8^{6}\times 8^{-9}\times 8^{9}\times 8^{-4}\)
- step3: Multiply the terms:
\(8^{6-9+9-4}\)
- step4: Calculate:
\(8^{2}\)
- step5: Evaluate the power:
\(64\)
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución Mind Expander
To solve the expression, we'll simplify it step by step. First, apply the quotient rule of exponents, which states that \( \frac{a^m}{a^n} = a^{m-n} \). 1. Simplifying \( \frac{8^{6}}{8^{9}} \): \[ \frac{8^{6}}{8^{9}} = 8^{6-9} = 8^{-3} \] 2. Next, simplify \( \frac{8^{9}}{8^{4}} \): \[ \frac{8^{9}}{8^{4}} = 8^{9-4} = 8^{5} \] 3. Now combine the results: \[ 8^{-3} \times 8^{5} = 8^{-3+5} = 8^{2} \] 4. Finally, calculate \( 8^{2} \): \[ 8^{2} = 64 \] So, \( \frac{8^{6}}{8^{9}} \times \frac{8^{9}}{8^{4}} = 64 \).
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