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ACT Aspire Math: Taking Shortcuts with Exponent Properties 2 Views


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Description:

What is the value of (-2)⁶?


Transcript

00:01

Okay Shmoop math people Here we go Another drill for

00:04

you What is the value of the quantity Negative to

00:08

to the sixth power All right let's think about this

00:15

one The most straightforward way to perform this kind of

00:17

calculation would be to multiply negative too by itself Six

00:20

times But well that's not terribly efficiently Not all the

00:24

time Instead we can use the properties of exponents to

00:26

take a shortcut Well the power rule for exponents tells

00:29

us that when one term with exponents is raised to

00:32

another exponents weaken simplify the expression by multiplying the two

00:35

exponents In other words x to the a power that

00:38

quantity to the b is the same as x to

00:41

the quantity eight times be so we can use this

00:44

route change the problem so that we can work with

00:46

a familiar cube root and square root Familiar like we

00:50

know two squared for without really been thinking about it

00:52

Right So what does that give us Let's factor out

00:54

something's here we got negative two to the six that

00:56

quantity which is the same as negative too toothy three

01:01

times two which is the same as a double quantity

01:04

thing here negative two cubed and then square so if

01:08

we do all that out that gets us negative eight

01:11

squared right because two four eight would be to cuba

01:14

And then we've got negative to cube being negative eight

01:17

and negative Eight square to sixty four so negative to

01:20

to the sixth power is positive sixty four and negative

01:24

sixty four's and b might be tempting but it's incorrect

01:26

because any imager raised two and even power must be

01:30

a positive number So anyway that's it It's sixteen And

01:33

yes you could have brute force this one just as

01:35

easily But we're doing this says that the on the

01:37

exam when they give you to the seventeenth power in

01:39

the thirty fourth power you can kind of do it 00:01:42.163 --> [endTime] quicker and easier Hopefully good luck with that

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