Question
Question
Which of the following is the equivalent expression to (52 ⋅ 102)032
?(1 point)
Responses
279
2 and 7 ninths
16
1 sixth
19
1 ninth
278
278
Which of the following is the equivalent expression to (52 ⋅ 102)032
?(1 point)
Responses
279
2 and 7 ninths
16
1 sixth
19
1 ninth
278
278
Answers
GPT-4o mini
To solve the expression \( (52 \cdot 102)^{032} \), we first clarify that \( 032 \) is essentially \( 32 \) since leading zeros don't change the value of a number.
Now, let's calculate the expression step by step:
1. Calculate \( 52 \cdot 102 \):
\[
52 \cdot 102 = 52 \cdot (100 + 2) = 52 \cdot 100 + 52 \cdot 2 = 5200 + 104 = 5304
\]
2. Now, we interpret \( 5304^{32} \). However, since the given options seem to be representing a simple numerical expression rather than calculating a very large number, it seems there might be a misunderstanding in the question.
Since none of the provided options relate to the calculation in the way we've interpreted it, let’s consider them at face value:
- 279 (which is \( 279 \))
- 2 and 7 ninths (which is \( 2 + 7/9 \))
- 16 (which is \( 16 \))
- 1 sixth (which is \( 1/6 \))
- 19 and 1 ninth (which is \( 19 + 1/9 \))
- 278 (which is \( 278 \))
Without further context or clarification on how to interpret the \( (52 \cdot 102)^{032} \) into a simpler expression, it appears that answering this question requires more details.
If you are looking for a numerical equivalency of a simplified expression from the multiplication, it may imply a need to check which option is closest to an approximate or reducible fraction.
But as it stands from our earlier calculations:
Since \( 5304 \) does not connect clearly to the options provided, if there's no computational requirement or arithmetic reduction implied, I suggest checking the context of the question or confirming its details.
For correct numerical relations based upon the dimension of this, I could assert the option close to standard representations.
If we focus on numerically simplifying \( 5304 \) into decimal, I would suggest checking additional resources or verification to align with expected output formats. If you meant something distinct from pure multiplication and exponentiation, please clarify specifically how the base number transfers into required options provided.
As per calculations performed, none of the numerical options directly correlate with \( 5304^{32} \).
Now, let's calculate the expression step by step:
1. Calculate \( 52 \cdot 102 \):
\[
52 \cdot 102 = 52 \cdot (100 + 2) = 52 \cdot 100 + 52 \cdot 2 = 5200 + 104 = 5304
\]
2. Now, we interpret \( 5304^{32} \). However, since the given options seem to be representing a simple numerical expression rather than calculating a very large number, it seems there might be a misunderstanding in the question.
Since none of the provided options relate to the calculation in the way we've interpreted it, let’s consider them at face value:
- 279 (which is \( 279 \))
- 2 and 7 ninths (which is \( 2 + 7/9 \))
- 16 (which is \( 16 \))
- 1 sixth (which is \( 1/6 \))
- 19 and 1 ninth (which is \( 19 + 1/9 \))
- 278 (which is \( 278 \))
Without further context or clarification on how to interpret the \( (52 \cdot 102)^{032} \) into a simpler expression, it appears that answering this question requires more details.
If you are looking for a numerical equivalency of a simplified expression from the multiplication, it may imply a need to check which option is closest to an approximate or reducible fraction.
But as it stands from our earlier calculations:
Since \( 5304 \) does not connect clearly to the options provided, if there's no computational requirement or arithmetic reduction implied, I suggest checking the context of the question or confirming its details.
For correct numerical relations based upon the dimension of this, I could assert the option close to standard representations.
If we focus on numerically simplifying \( 5304 \) into decimal, I would suggest checking additional resources or verification to align with expected output formats. If you meant something distinct from pure multiplication and exponentiation, please clarify specifically how the base number transfers into required options provided.
As per calculations performed, none of the numerical options directly correlate with \( 5304^{32} \).