Question

What is the correct simplification of 243^3/5
?(1 point)
Responses

81
81
9
9
3
3
27

Answer 1

Let's simplify \( \frac{243^3}{5} \).

To find the value of \( 243^3 \), we first note that \( 243 = 3^5 \). Therefore, we can express \( 243^3 \) as:

\[
243^3 = (3^5)^3 = 3^{5 \cdot 3} = 3^{15}
\]

Next, we need \( \frac{3^{15}}{5} \).

Since it's not specified that we need a numerical value or if we should stop our calculation here, the expression \( \frac{3^{15}}{5} \) does not simplify further into a simple integer.

However, looking at the context of your responses, it seems that the option might involve roots or factors of \( 243 \), rather than the full power of \( 243^3 \).

If you're looking for \( \frac{243}{5} \):
- \( 243 \div 5 = 48.6 \), which does not match any of your options.

Thus, none of the provided options (81, 9, 3, 27) are correct simplifications of \( \frac{243^3}{5} \).

If the question is focusing on something else, such as finding possible integer factors of the form \( \frac{3^n}{5} \), that doesn't seem to fit the original expression.

If you meant \( 243^{\frac{3}{5}} \) instead, then:

\[
243^{\frac{3}{5}} = (3^5)^{\frac{3}{5}} = 3^3 = 27
\]

In that case, the correct answer would be **27**.

Please confirm the context of the original question for clarification.