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

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

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considered replacing our regularly scheduled programme solving programming with reruns

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from our youtube channel but it turns out that while

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people are more interested in how to simplify algebraic expressions

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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

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All right so asking you shall receive while there are

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many ways to begin simplifying this gnarly crazy exponential expression

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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

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

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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

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going to do is just move everything here flip flop

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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

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us What is that twenty r cubed And here And

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then in six r squared plus once we add the

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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

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s to the first there on the exam They may

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not be so kind so that gets us as to

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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

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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

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

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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

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

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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

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

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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

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