Pregunta
Simplify to a single power of 4: \[ \left(4^{4}\right)^{5} \]
Ask by Donnelly Smith. in the United States
Mar 11,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The simplified expression is \(4^{20}\).
Solución
We start with the expression:
\[
\left(4^4\right)^5
\]
Using the power-of-a-power rule, we have:
\[
\left(4^4\right)^5 = 4^{4 \cdot 5}
\]
Multiplying the exponents gives:
\[
4^{4 \cdot 5} = 4^{20}
\]
Thus, the simplified expression is:
\[
4^{20}
\]
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Simplifique esta solución Beyond the Answer
To simplify \(\left(4^{4}\right)^{5}\), we can use the power of a power property of exponents, which states that \((a^{m})^{n} = a^{m \cdot n}\). Applying this property here, we have: \[ \left(4^{4}\right)^{5} = 4^{4 \cdot 5} \] Calculating the exponent: \[ 4 \cdot 5 = 20 \] Thus, we find: \[ \left(4^{4}\right)^{5} = 4^{20} \] So, the simplified expression is: \[ 4^{20} \]
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