# 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 Assessment TSI Math TSI Mathematics |

TSI Math | Intermediate Algebra and Functions |

TSI Mathematics | Intermediate Algebra and Functions |

Test Prep | TSI |

### Transcript

than they are in watching us create scale models of

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

All right so asking you shall receive while there are

many ways to begin simplifying this gnarly crazy exponential expression

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

to make the exponents positive move the variable to the

opposite location in the fraction variables in the numerator go

to the denominator and variables in the denominator go to

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

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

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

going to do is just move everything here flip flop

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

simplified by multiplying variable terms with the same bases together

When this happens the exponents are added so that gets

us What is that twenty r cubed And here And

then in six r squared plus once we add the

two in the one there when we have in our

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

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

s to the first there on the exam They may

not be so kind so that gets us as to

the fifth here on the bottom And then we got

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

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

fifth All right so this is way simpler here Twenty

r cubed over ten r squared as to the fifth

plus six r cubed over eight s to the fifth

So next up when dividing factors with like bases like

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

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

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

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

from down here to get rid of it So what

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

twenty art of the first Well over ten as to

the fifth and then six r q P o radius

Okay well so what else can we do here tio

Simplify things Well finally we can simply the coefficients of

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

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

zeros there Twenty over ten becomes too over one And

just two And the six over eight There becomes three

force So we got two r over us to the

fifth plus three r cubed over for s to the

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

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

the same as this Eight are over us and so

on Equation on d there which is one big hint

The fractions should be added Multiply the first fraction by

four over four to create a common denominator of four

ass to the fifth See how clever that is So

we can go for over four times as so we

get eight And then plus the three are there over

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

of a luxury around here So what does that Give

us well added new rangers Crossed top and simplest expression

is b eight are plus three r cubed over for

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