To solve the equation [tex]\( p^3 = 125 \)[/tex], follow these steps:
1. Identify the equation: We begin with the equation [tex]\( p^3 = 125 \)[/tex].
2. Express 125 as a power of a simpler number:
[tex]\[
125 = 5^3
\][/tex]
3. Set up the equation with equivalent powers:
[tex]\[
p^3 = 5^3
\][/tex]
4. Since the powers are equal, the bases must also be equal:
[tex]\[
p = 5
\][/tex]
So the real solution to the equation [tex]\( p^3 = 125 \)[/tex] is [tex]\( p = 5 \)[/tex].
Now, let us analyze the provided choices:
- (A) [tex]\( p = 3 \)[/tex]
- (B) [tex]\( p = -3 \)[/tex]
- (C) [tex]\( p = 6 \)[/tex]
- (D) [tex]\( p = -6 \)[/tex]
- (E) None of the above
Comparing each choice with our solution [tex]\( p = 5 \)[/tex]:
- [tex]\( p = 3 \)[/tex] (A): [tex]\( 3^3 = 27 \)[/tex], not equal to 125.
- [tex]\( p = -3 \)[/tex] (B): [tex]\( (-3)^3 = -27 \)[/tex], not equal to 125.
- [tex]\( p = 6 \)[/tex] (C): [tex]\( 6^3 = 216 \)[/tex], not equal to 125.
- [tex]\( p = -6 \)[/tex] (D): [tex]\( (-6)^3 = -216 \)[/tex], not equal to 125.
Since none of these choices are equal to 125, the correct answer must be:
- (E) None of the above
Therefore, the correct answer is:
(E) None of the above
