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

Simplify the following expression. Intermediate Algebra and Functions Rational and Exponential Expressions, Equations, and Functions Mathematics and Statistics Assessment Rational and Exponential Expressions, Equations, and Functions Product Type TSI TSI Mathematics and Statistics AssessmentTSI MathTSI Mathematics TSI Math Intermediate Algebra and Functions TSI Mathematics Intermediate Algebra and Functions Test Prep TSI

### Transcript

00:23

than they are in watching us create scale models of

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

00:29

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

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to make the exponents positive move the variable to the

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opposite location in the fraction variables in the numerator go

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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

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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

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simplified by multiplying variable terms with the same bases together

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When this happens the exponents are added so that gets

01:11

us What is that twenty r cubed And here And

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then in six r squared plus once we add the

01:16

two in the one there when we have in our

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

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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

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

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

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fifth All right so this is way simpler here Twenty

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r cubed over ten r squared as to the fifth

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plus six r cubed over eight s to the fifth

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So next up when dividing factors with like bases like

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

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

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

01:52

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

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from down here to get rid of it So what

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

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twenty art of the first Well over ten as to

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the fifth and then six r q P o radius

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Okay well so what else can we do here tio

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Simplify things Well finally we can simply the coefficients of

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

02:15

02:18

zeros there Twenty over ten becomes too over one And

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just two And the six over eight There becomes three

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force So we got two r over us to the

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fifth plus three r cubed over for s to the

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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

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on Equation on d there which is one big hint

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The fractions should be added Multiply the first fraction by

02:45

four over four to create a common denominator of four

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ass to the fifth See how clever that is So

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we can go for over four times as so we

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get eight And then plus the three are there over

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03:00

of a luxury around here So what does that Give

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us well added new rangers Crossed top and simplest expression

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is b eight are plus three r cubed over for

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