Question

relate the expressions $2^6$ and $4^4$ to their equivalent expanded or simplified forms, with options like $4\cdot4\cdot4$, $64\cdot4$, $16\cdot16$, $4\cdot4\cdot16$, $4\cdot4\cdot4\cdot4$, and $8\cdot8$ shown in the image.

Explanation:

Step1: Calcular \(2^6\)

\(2^6 = 2\times2\times2\times2\times2\times2 = 64\)

Step2: Calcular \(4^4\)

\(4^4 = 4\times4\times4\times4 = 256\)

Step3: Analizar las opciones

• \(4\cdot4\cdot4 = 64\) (no es igual a \(256\))
• \(64\cdot4 = 256\) (igual a \(4^4\))
• \(16\cdot16 = 256\) (igual a \(4^4\))
• \(4\cdot4\cdot16 = 256\) (igual a \(4^4\))
• \(4\cdot4\cdot4\cdot4 = 256\) (igual a \(4^4\))
• \(8\cdot8 = 64\) (no es igual a \(256\))

Answer:

Las expresiones equivalentes a \(4^4\) son: \(64\cdot4\), \(16\cdot16\), \(4\cdot4\cdot16\), \(4\cdot4\cdot4\cdot4\)