Question

What is the sign of

\[-3\cdot\dfrac{4}{(-7)^{105}}\]?
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

\[
-3 \cdot \dfrac{4}{(-7)^{105}},
\]

let's analyze each component of the expression.

1. **The term \(-3\)**: This is negative.
2. **The denominator \((-7)^{105}\)**: Since the exponent (105) is odd, \((-7)^{105}\) will also be negative (specifically, a large negative number).

Now, we can look at the fraction \(\dfrac{4}{(-7)^{105}}\):

- The numerator, \(4\), is positive.
- The denominator, \((-7)^{105}\), is negative.

So, the fraction \(\dfrac{4}{(-7)^{105}}\) will be negative (a positive number divided by a negative number results in a negative number).

Now we have:

\[
-3 \cdot \text{(a negative number)}.
\]

Multiplying a negative number \(-3\) by a negative fraction results in a positive product:

\[
-3 \cdot \text{(negative)} = \text{positive}.
\]

Thus, the sign of the entire expression is positive.

The answer is:

**(Choice A) Positive**.