Question

¿qué expresión es equivalente a $2(8n)^4$?
$2 \cdot 8n \cdot 8n \cdot 8n \cdot 8n$
$(2 \cdot 8n)(2 \cdot 8n)(2 \cdot 8n)(2 \cdot 8n)$
$2 \cdot 8 \cdot n \cdot n \cdot n \cdot n$
$2 \cdot 8 \cdot 4$

Explanation:

Step1: Recall exponent definition

An expression \(a^b\) means \(a\) multiplied by itself \(b\) times. So \((8n)^4 = 8n \cdot 8n \cdot 8n \cdot 8n\).

Step2: Analyze the original expression

The original expression is \(2(8n)^4\), so we multiply the result of \((8n)^4\) by 2. Substituting the expansion of \((8n)^4\), we get \(2 \cdot 8n \cdot 8n \cdot 8n \cdot 8n\).

Step3: Analyze other options

• The second option expands \((2\cdot8n)^4\), not \(2(8n)^4\).
• The third option incorrectly simplifies \(8^4\) as 8 and \(n^4\) as \(n\cdot n\cdot n\cdot n\) but misses the repeated multiplication of 8.
• The fourth option is incorrect as it doesn't relate to the exponentiation of \(8n\).

Answer:

\(2 \cdot 8n \cdot 8n \cdot 8n \cdot 8n\)