Pregunta
Simplify the given expression below. Leave the answer in exponential notation, \( (6 w)^{2} \cdot\left[(6 w)^{8}\right]^{4} \)
Ask by Powers Simpson. in the United States
Jan 27,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\(6^{34}w^{34}\)
Solución
Calculate or simplify the expression \( (6w)^2 * ((6w)^8)^4 \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(6w\right)^{2}\left(\left(6w\right)^{8}\right)^{4}\)
- step1: Multiply the exponents:
\(\left(6w\right)^{2}\left(6w\right)^{8\times 4}\)
- step2: Multiply the numbers:
\(\left(6w\right)^{2}\left(6w\right)^{32}\)
- step3: Rewrite the expression:
\(36w^{2}\times 6^{32}w^{32}\)
- step4: Multiply the numbers:
\(6^{34}w^{2}\times w^{32}\)
- step5: Multiply the terms:
\(6^{34}w^{34}\)
The simplified expression is \(6^{34}w^{34}\).
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Simplifique esta solución Beyond the Answer
To simplify the expression \( (6 w)^{2} \cdot\left[(6 w)^{8}\right]^{4} \), you first simplify \(\left[(6 w)^{8}\right]^{4}\) using the power of a power rule, which states that \((a^{m})^{n} = a^{m \cdot n}\). Thus, \(\left[(6 w)^{8}\right]^{4} = (6 w)^{32}\). Now we have: \[ (6 w)^{2} \cdot (6 w)^{32} \] Using the product of powers rule, we can add the exponents: \[ (6 w)^{2 + 32} = (6 w)^{34} \] So, the simplified expression is \((6w)^{34}\).
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