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TSI Math: Using Every Trick in the Box to Simplify an Expression 0 Views


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Description:

Simplify the following expression.


Transcript

00:02

Okay sy mass Shmoop er's simplify the following expression Okay

00:09

uh this one's really ugly Oh my goodness So we

00:13

considered replacing our regularly scheduled programme solving programming with reruns

00:18

from our youtube channel but it turns out that while

00:20

people are more interested in how to simplify algebraic expressions

00:23

than they are in watching us create scale models of

00:26

famous landmarks using pasta weird we're so good at that

00:29

All right so asking you shall receive while there are

00:31

many ways to begin simplifying this gnarly crazy exponential expression

00:36

but well here we're going to eliminate negative exponents first

00:39

to make the exponents positive move the variable to the

00:43

opposite location in the fraction variables in the numerator go

00:47

to the denominator and variables in the denominator go to

00:50

the numerator see how we do this here So we've

00:52

got well that we're starting with the twenty are the

00:55

negative too and then ethan and stuff and then we're

00:58

going to do is just move everything here flip flop

01:01

so we've got this ugly beast right here so we

01:04

simplified by multiplying variable terms with the same bases together

01:07

When this happens the exponents are added so that gets

01:11

us What is that twenty r cubed And here And

01:14

then in six r squared plus once we add the

01:16

two in the one there when we have in our

01:17

times and our down here we've gotten as to the

01:20

first honest to the force it's nice They put the

01:23

s to the first there on the exam They may

01:24

not be so kind so that gets us as to

01:27

the fifth here on the bottom And then we got

01:29

as to the third And as to the second there's

01:31

what's going on adam And that consists s to the

01:33

fifth All right so this is way simpler here Twenty

01:35

r cubed over ten r squared as to the fifth

01:38

plus six r cubed over eight s to the fifth

01:40

So next up when dividing factors with like bases like

01:44

you know the r's and the first fraction there subtract

01:47

the exponents so we can actually do that that's legal

01:49

even in even in texas So we've got twenty are

01:52

cube there and we're just going to subtract the two

01:55

from down here to get rid of it So what

01:58

does that make it All right so then we've got

01:59

twenty art of the first Well over ten as to

02:02

the fifth and then six r q P o radius

02:04

Okay well so what else can we do here tio

02:08

Simplify things Well finally we can simply the coefficients of

02:12

each fraction is if they didn't have dedicated variable followers

02:15

Right So let's think about this Just cross out the

02:18

zeros there Twenty over ten becomes too over one And

02:21

just two And the six over eight There becomes three

02:23

force So we got two r over us to the

02:26

fifth plus three r cubed over for s to the

02:29

fifth Okay so that's about as simple as we can

02:32

get but we're not done The simplified expression is not

02:35

the same as this Eight are over us and so

02:39

on Equation on d there which is one big hint

02:42

The fractions should be added Multiply the first fraction by

02:45

four over four to create a common denominator of four

02:49

ass to the fifth See how clever that is So

02:51

we can go for over four times as so we

02:53

get eight And then plus the three are there over

02:57

four Asked to the fifty weaken adam that's that's Kind

03:00

of a luxury around here So what does that Give

03:02

us well added new rangers Crossed top and simplest expression

03:04

is b eight are plus three r cubed over for

03:07

ass to the fifth Okay we're done We're shmoop

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