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A detailed tutorial on how to solve negative exponents. Step by step tutorial including several examples of solving negative exponents for reference.

An exponent is a number representing how many times you multiply the base – the number the exponent is on – by itself. Which is why negative exponents are so confusing – how can you multiply something by itself a negative number of times? The easiest way to think of a negative exponent, is that if you take away the negative sign and put the base and exponent under the number 1 (like as a fraction), you are saying the same thing! A negative exponent simply needs to be moved to the denominator (or the numerator, if it is in the denominator) to make it a positive exponent. This can be tricky when there are other numbers or expressions found in the same fraction, but not impossible.

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A detailed tutorial on degrees of polynomials. Step by step tutorial including several examples of degrees of polynomials for reference.

The degree of a polynomial is the highest power found in it. For example, in your normal quadratic equation, the degree is two, because the highest power – the highest number found in an exponent – is a two. In other polynomials, the degree may be something different. No matter what order the variables and their powers are placed in, the degree is always the highest one. For example. the degree of x^2 + x + 7 is exactly the same as x + 7 + x^2.

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A detailed tutorial on higher order derivatives. Step by step tutorial including several examples of higher order derivatives for reference.

A higher order derivative is a derivative with a power other than one – that is, a derivative is referred to as a first derivative, and the higher order derivatives are a second derivative, third derivative, etc. The second derivative is the derivative of the first derivative, and the third derivative is the derivative of the second derivative. When you know all the rules of taking derivatives, taking second and third derivatives are simple. Simply take the derivative and pretend it is another equation. When you go up beyond the third derivative this can get more challenging, as there will be many more parts to the equation.

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A detailed tutorial on the introduction to relations. Step by step tutorial including several examples of the introduction to relations for reference.

A relation is defined as an ordered pair. However, that is not entirely accurate. A relation could either be an ordered pair or a set of ordered pairs.  A relation can be used with either one or more normal sets, or one Cartesian product set. When used with a normal set, it is a set of ordered pairs. When used with a Cartesian product, it is the power set of that set.

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A detailed tutorial on power sets. Step by step tutorial including several examples of power sets and how to perform operations of power sets  for reference.

Power sets are defined as a set of all subsets. So for example, say you have a set A. The power set of A would be the set of all possible subsets of A. Power sets can also be used in normal operations, such as intersections and unions. All you do is find all possible subsets of both sets you are working with, and solve the problem like you would with a normal set.

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A detailed tutorial on the solving of problems using the binomial theorem. Stepby step tutorial including several examples of how to solve problems using the binomial theorem for reference.

The binomial theorem is something you should all be familiar with – it is the alternative to the F.O.I.L. technique. It is used when you are given a binomial that is raised to a power. The simplest version of it is expressed like this:

This can also be expressed as a factorial notation, in the form:

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Description

This video explains both the Power Rule and the Constant Rule in-depth, and illustrates the difference between different functions with power rules on a graph. It provides several example problems that could be solved using the power rule.

Overview

The Power Rule is a rule in calculus that allows you to solve derivatives. The Power Rule deals with exponents, or powers. The simple power rule states that:

d/dx (x^n) = nx^(n – 1)

In other words, the number of the exponent gets placed in front of x, and then the exponent gets subtracted by 1. An interesting thing about the Power Rule is the \”chain of command\”. The power rule will be easier to use if you memorize this:

d/dx (x^0) = 0

d/dx (x^1) = 1

d/dx (x^2) = 2x

d/dx (x^3) = 3x^2