Question

What is the sign of

\[\dfrac{s^{67}}{t^9}\] when
\[s < 0\] and
\[t >0\] ?
Choose 1 answer:
Choose 1 answer:
(Choice A) Positive
A
Positive
(Choice B) Negative
B
Negative
(Choice C) Zero
C
Zero

Answer 1

To determine the sign of the expression

\[
\dfrac{s^{67}}{t^9}
\]

given that \( s < 0 \) and \( t > 0 \), we need to analyze the signs of the numerator and denominator separately.

1. **Numerator: \( s^{67} \)**:
- Since \( s < 0 \) and the exponent \( 67 \) is an odd number, \( s^{67} \) will also be negative. Thus, \( s^{67} < 0 \).

2. **Denominator: \( t^9 \)**:
- Since \( t > 0 \) and the exponent \( 9 \) is positive, \( t^9 \) will be positive. Thus, \( t^9 > 0 \).

Now combining these:

\[
\dfrac{s^{67}}{t^9} = \dfrac{\text{(negative)}}{\text{(positive)}} = \text{negative}
\]

Therefore, the sign of \( \dfrac{s^{67}}{t^9} \) is negative.

The correct answer is:

**(Choice B) Negative**