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 rule

The exponent \(a^b\) means \(a\) multiplied by itself \(b\) times. For \((8n)^4\), this is \(8n\times8n\times8n\times8n\).

Step2: Multiply by the coefficient

The original expression is \(2(8n)^4\), so we multiply the result from Step 1 by 2, giving \(2\times8n\times8n\times8n\times8n\).

Step3: Analyze other options

• The second option incorrectly applies the exponent to 2 as well, it should be \((8n)^4\) not \((2\cdot8n)^4\).
• The third option incorrectly simplifies \(8^4\) to 8, \(8^4 = 8\times8\times8\times8

eq8\).

• The fourth option ignores the variable \(n\) and misinterprets the exponent, \(4\) is not a multiplier in that way.

Answer:

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