When a positive number is raised to a positive power the result is always?

Since a positive number raised to a positive exponent is positive and the reciprocal of a positive number is positive. We have that x−y is positive. So we have shown why we can write x−y as 1xy.

When n is any odd positive integral power?

If n is an odd positive integer, then (-1) ^n is always negative.

How do you represent an odd number in proof?

Proof: Let x be an arbitrary odd number. By definition, an odd number is an integer that can be written in the form 2k + 1, for some integer k. This means we can write x = 2k + 1, where k is some integer. So x2 = (2k + 1)2 = 4k2 + 4k + 1 = 2(2k2 + 2k) + 1.

What is the power of odd numbers?

It means that whenever you are listing the benefits of your product or service, choose an odd number of benefits. If you are offering a series of bonuses, offer one or three, not two or four.

What is true about a positive integer raised to a negative integer power?

An integer raised to a negative power is always a positive fraction .

What is always true about a positive integer raised to a negative integer power *?

A number raised to a negative power is equal to one over the number raised to the positive opposite power. Example: x^-2 = 1/x^2.

Is divisible by 8 if’n is an odd positive integer?

Hence, we can easily conclude that ${n}^2 – 1$ is divisible by 8 for any odd positive odd integer. Complete step by step answer: Any odd positive number is in the form of (4p + 1) or (4p + 3) for some integers p. Hence, ${n^2} – 1$ is divisible by 8 if n is an odd positive integer.

How do you prove something is positive?

Starts here4:32How to Prove that a Quadratic Function is Always Positive (or …YouTube

How do you prove an even number?

Starts here3:04How to Prove a Number is Even – YouTubeYouTube

Is a negative number raised to an even power negative or positive?

Zero raised to the power of zero is undefined. When a negative number is raised to an even number power, the result will be a positive number. When a negative number is raised to an odd number power, the result will be a negative number. Each of these is illustrated with examples.

Are all powers of 3 odd?

Note that any power of 3 is an odd number. An odd number plus an odd number cannot equal an odd number.