What is the value of $(-3)^{5}$?
A$-243$
B$-15$
C$15$
D$243$
Answer & Solution
Correct answer: A. $-243$
A negative number raised to an **odd** power is **negative**:
$(-3)^{5} = (-3)(-3)(-3)(-3)(-3) = 9 \cdot (-3) \cdot 9 = 243 \cdot (-1) = -243$.
Step by step: $(-3)^{2} = 9$, $(-3)^{3} = -27$, $(-3)^{4} = 81$, $(-3)^{5} = -243$.
- Trap D ($243$) treats the exponent as if it were even.
- Trap B/C ($\pm 15 = -3 \times 5$) confuses exponentiation with multiplication.
Rule: $(-x)^{n}$ is positive iff $n$ is even.
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