Give the answer to the question. Let k be a natural number. Is ( - 5 ) ²^k^{+ 1} positive or negative? A) positive B) undefinable number C) negative

Question

Quizplus · Accepted Answer

We can simplify the expression using the order of operations (PEMDAS):
- First, evaluate any expressions inside parentheses or brackets. There are none in this case.
- Next, evaluate any exponential expressions. There are none.
- Moving from left to right, perform any multiplication or division. There is no multiplication or division.
- Finally, moving from left to right, perform any addition or subtraction.

When we add ( - 5 ) S1U1P12S1S1P0S1U1P1kS1S1P0S1U1P1 + 1S1S1P0, we are essentially combining two different base-14 numbers. We start by adding the units (i.e. the ones) place, which gives us:

0 (carrying over 1 to the 14s place)

Next, we add the 14s place:

1 + 1 = 2

So far, the sum is 20 (in base-14), which is equivalent to 28 in base-10.

Continuing this process, we find that the expression simplifies to:

( - 28 ) S1U1P1kS1S1P0S1U1P1

Since k is a natural number, which includes 1, 2, 3, etc., we know that S1U1P1k will always represent a number greater than or equal to 1. Therefore, the entire expression evaluates to a negative number, making the answer negative (choice C).

Give the Answer to the Question