TSI Math: Simplifying Fractions with a Ton of Exponents

Simplify the following expression.

Intermediate Algebra and FunctionsRational and Exponential Expressions, Equations, and Functions
Mathematics and Statistics AssessmentRational and Exponential Expressions, Equations, and Functions
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Transcript

00:20

power or experiment number there Yeah well the extra exponents

00:23

are knocked out by the power to a power rule

00:26

right When exponential expressions are raised to a power we

00:30

can multiply the exponents together That'll help us a whole

00:34

lot here All right so we're going to do some

00:36

multiple in here so well let's start with this one

00:39

So we've got x word y to the second power

00:41

which is the same as x squared times two and

00:44

then times y to the one times two thinking there

00:47

and then on the bottom here we got this thing

00:49

cubed that's going to be the same as x to

00:52

the three times three And why did the two times

00:54

three and let's just go do all the arithmetic here

00:57

So we got xs seventh wanted seventh over x to

00:59

the ninth one of the six and all this stuff

01:01

Okay bam How the expression is starting to shrink Hey

01:05

it's good Use that x ray vision to identify expressions

01:07

that cancel in the first term of six wise in

01:10

the denominator cancel with six of the seven wise in

01:13

the numerator leaving just one behind you is gonna look

01:16

like this Why right there why over x squared Is

01:19

it The seven x is in the numerator Cancel seven

01:22

of the nine x is in the denominator leading just

01:25

two exes They're cease oh that's way simpler Why over

01:28

x squared that's What All this stuff up here reduced

01:30

down teo Yeah so it's kind of good All right

01:33

so let's keep going Now the second fraction this one

01:35

is identical in the numerator and denominator so the entire

01:39

fractions just one that's it it's Why over x squared

01:42

plus one after all that work Yep Are super human

01:46

ability to use exponents rule to fight evil one simplified

01:49

expressions leaves us to truth justice and the shmoop way 00:01:52.663 --> [endTime] Yeah so why over x y plus one