Fundamentals of Engineering Exam Review of Power Functions

In this episode of Engineer In Training Exam TV, Justin walks you through a Fundamentals of Engineering Exam Review of Power Functions.

The goal is to reinforce both your understanding of the various rules of power functions, but also to put this knowledge to work through a few example problems.

This Fundamentals of Engineering Review of Power Functions is part of the global subject Mathematics.

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Transcription

Hey what’s gong on everyone, it’s Justin Dickmeyer from EngineerInTrainingExam.com.

In today’s video we are going to present a Fundamentals of Engineering Exam Review Of Power Functions.

There are some essential rules of power functions that we must be familiar with in order to greatly simplify the solving of these complex equations.

So let’s start off our Fundamentals of Engineering Exam Review Of Power Functions by defining exactly what a Power Function is.

A power function takes the

form Y is equal to a raised to the X

where a is known as the base and X is

known as the power or the exponent both

interchangeable terms

now when given a power function and that

power function strays away from this

standard form we can dig into our bag of

tricks to simplify using a list of rules

the first rule is the power of products

say we are given a power function where

the base is made up of a product of two

numbers say a times B and that base is

then raised to the X power

given a function in this form it can be

re-written as a raised to the x times B

raised to the X now if we’re given a

function as a product of two power

functions of the same base being raised

to different powers such as a raised to

the x times a raised to the W this can

be rewritten by taking the exponents

adding them together and setting them

against the common base so in other

words we can rewrite this as a x + W now

what if we’re given a function where one

power function is being divided by a

another power function of the same base

similar as before say we have a raised

to the X divided by a raised to the W

well the rule here is that this function

can be rewritten by taking the exponents

and subtracting them from one another

and setting that against the common base

so in other words you can rewrite it as

a raised to the X minus W now if the

base of itself is a power function and

is raised then again by another power

say a raised to the W and that’s raised

to the X this can be rewritten by

multiplying the exponents together and

setting it against the original base so

in other words it can be re-written as a

raised to the W times X now all these

rules right here we’re dealing with

positive exponents but all numbers are

possible in power functions so let’s

look at the special cases when the

exponents are equal to 0 1 are negative

or even non integer rational numbers

such as fractions so first we can note

that any base raised to the power of 0

is 1 so if we the rule here the special

rule the power of 0 if we have any base

and it’s raised to the 0 that is going

to be equal to 1 now let’s talk about

the power of power of 1 rule any base

raised to the power 1 means that that

base is being multiplied only once by

itself so that means that a raised to

the 1 is equal to itself a it’s only

it’s only multiplied once but what about

negative numbers how do we deal with

negative exponents well we determined

that when given a function where one

power function is being divided by

another power function of the same base

if you recall a X divided by aw that the

function can be rewritten by subtracting

the exponents and setting them against

the common base so in other words a X

minus W so we’ve already established

that but what happens when W in the

denominator the power in the denominator

is larger than the power in the

numerator

well since the larger exponent is on the

bottom it shouldn’t be a surprise that

the beta U that the base raised to a

negative exponent can be re-written as a

raised to the say negative W is actually

rewritten as a over so r1 divided by a

raised to the W so in other words we can

quickly illustrate this let’s say that

we have a squared divided by a to the

third if you just expand this out that

will be a times a in the in the

numerator and we got a times a times a

in the denominator and now common terms

cancel out so we got two A’s on the

bottom that cancel out two A’s on the

top one remains on the just the number

one remains on the top and so now we

have 1 over a which is also equivalent

to a to the negative one so now lastly

let’s look at let’s look at the dreaded

fractions when a base is raised to a

fraction let’s say 1 to the N for

definition purposes that function can be

rewritten as the nth root of a

such as say if we have won a raised to

one to the end can be re-written as the

nth root of a but the fraction doesn’t

have to be one over some variable it can

be anything such as two thirds or five

six

so let’s generalize this by saying that

if we are given a function raised to M

in a raised to the M over n then that

function can be re-written as the nth

root of a raised to the M so that’s

going to be our general equation so for

given any function let’s just look at

one right real quick let’s say we have 5

raised to the one-sixth well that can

simply be re-written as 6 the sixth root

of 5 raised to the 1 and once again that

wine could be 3 could be 4 or 5 whatever

number is on top it doesn’t have to be

one that’s just M so lastly I want to

touch on one particular base which is of

singular importance in math and that is

the transcendental number or e which is

written as E and that’s equal to two

point seven one eight two and and change

it keeps going this base shows up

naturally and calculates because the

power of the base is equal to its own

derivative so in other words if we’re

given the function e to the X the

derivative of that dy/dx is also equal

to e to the X the base power a function

either the X is called the exponential

function and is sometimes abbreviated as

exp such that e each of X is equal to e

XP X so you might see the exponential

function

written in either of these two ways so

that will wrap up the review of the

power functions if you guys have any

Power Functions – Fundamentals of Engineering Exam Review

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