4.2 & $$ \begin{array}{l} ext { Is the statement true or false. If the statement is false rewrite it as a } \ ext { correct statement. } \ 6^{8}=2^{4} imes 3^{4}\end{array} $$

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4.2 & $$ \begin{array}{l}	ext { Is the statement true or false. If the statement is false rewrite it as a } \ 	ext { correct statement. } \ 6^{8}=2^{4} 	imes 3^{4}\end{array} $$

UpStudy AI · Accepted Answer

The statement is **false**.

**Correct Statement:**
$$ 6^{8} = 2^{8} \times 3^{8} $$

**Explanation:**
The original statement claims that $$6^8$$ is equal to $$2^4 \times 3^4$$. Let's evaluate both sides:

- **Left Side:** 
  $$ 6^{8} = (2 \times 3)^{8} = 2^{8} \times 3^{8} $$
  
- **Right Side:** 
  $$ 2^{4} \times 3^{4} = 16 \times 81 = 1296 $$
  
However, $$6^{8}$$ is:
$$ 6^{8} = 1679616 $$
  
Clearly, $$1679616 \neq 1296$$, so the original statement is incorrect. The correct relationship maintains the exponent for each prime factor:

$$ 6^{8} = 2^{8} \times 3^{8} $$
The statement is false. The correct statement is $$6^{8} = 2^{8} \times 3^{8}$$.

4.2 & \( \begin{array}{l}\text { Is the statement true or false. If the statement is false rewrite it as a } \\ \text { correct statement. } \\ 6^{8}=2^{4} \times 3^{4}\end{array} \)

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