Question
jenny is working on simplifying the algebraic expression 3^x + 21 when x = 5 her steps as follows
step 1: 3^5 + 21
step 2: 15 + 21
step 3: 36
in which step did jenny make a mistake? what should she have done differently?
step 1: 3^5 + 21
step 2: 15 + 21
step 3: 36
in which step did jenny make a mistake? what should she have done differently?
Answers
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Answered by
GPT-4o mini
Jenny made a mistake in step 2. In step 1, she correctly substituted \( x = 5 \) into the expression, calculating \( 3^5 \).
In step 2, instead of calculating \( 3^5 \) correctly, she incorrectly stated that \( 3^5 = 15 \).
The correct calculation for \( 3^5 \) is:
\[
3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243
\]
Thus, the correct steps should have been:
1. \( 3^5 + 21 \)
2. \( 243 + 21 \)
3. \( 264 \)
So the correct final result should be \( 264 \). Jenny should have correctly computed \( 3^5 \) instead of incorrectly assuming it was \( 15 \).
In step 2, instead of calculating \( 3^5 \) correctly, she incorrectly stated that \( 3^5 = 15 \).
The correct calculation for \( 3^5 \) is:
\[
3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243
\]
Thus, the correct steps should have been:
1. \( 3^5 + 21 \)
2. \( 243 + 21 \)
3. \( 264 \)
So the correct final result should be \( 264 \). Jenny should have correctly computed \( 3^5 \) instead of incorrectly assuming it was \( 15 \).
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