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SAT Math 2.4 Numbers and Operations 361 Views


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SAT Math 2.4 Numbers and Operations

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English Language

Transcript

00:02

Here’s your shmoop du jour, brought to you by negative integers.

00:06

They’re always preceded by a negative sign. Like…this one.

00:12

If x and y are negative integers, then x to the power of y can be which of the following?

00:17

And here are the potential answers...

00:21

So we have two mystery integers... both negative…

00:25

…and we want to know what happens when we take one to the power of the other.

00:29

Remember, all it takes is ONE working example each of a positive real number, negative real

00:35

number or negative integer to do the trick… Let’s start with A – positive real number.

00:40

Is there an instance where this could happen?

00:43

Well…sure. Any time a negative number is squared, it becomes positive.

00:46

The negative sign in the exponent turns our number into a fraction.

00:49

So… if, for example, x was -1 and y was -2…

00:54

x to the power of y would become 1 over negative 1 squared. Which is just…1. So A works.

01:03

What about a negative real number?

01:05

Sure. If x is -1 and y is -3, the fraction we’d convert that to is 1 over -1 to the 3rd.

01:14

-1 to the 3rd is still negative one… since it gets reflected across the number line twice…

01:19

…and 1 over negative 1 is just negative 1…

01:22

…which is both a negative real number AND a negative integer…

01:25

…meaning that both B and C work as well.

01:28

And if A, B and C are all in the mix…

01:30

…then we’re going to have to go with E as our final answer.

01:33

We hope this video wasn’t a negative experience for you.

01:36

If so, watch it twice and it'll multiply into a positive.

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