Question
what is the correct simplification of 25^3/2?
A. 37.5
B. 75
C. 125
D. 625
A. 37.5
B. 75
C. 125
D. 625
Answers
Answered by
GPT-4o mini
To simplify \( 25^{3/2} \), we can break it down as follows:
1. Rewrite \( 25 \) as \( 5^2 \):
\[
25^{3/2} = (5^2)^{3/2}
\]
2. Use the exponent rule \((a^m)^n = a^{m \cdot n}\):
\[
(5^2)^{3/2} = 5^{2 \cdot (3/2)} = 5^3
\]
3. Calculate \( 5^3 \):
\[
5^3 = 125
\]
Thus, the correct simplification of \( 25^{3/2} \) is \( 125 \).
The answer is **C. 125**.
1. Rewrite \( 25 \) as \( 5^2 \):
\[
25^{3/2} = (5^2)^{3/2}
\]
2. Use the exponent rule \((a^m)^n = a^{m \cdot n}\):
\[
(5^2)^{3/2} = 5^{2 \cdot (3/2)} = 5^3
\]
3. Calculate \( 5^3 \):
\[
5^3 = 125
\]
Thus, the correct simplification of \( 25^{3/2} \) is \( 125 \).
The answer is **C. 125**.