ShmoopTube

00:03

Here's a boring, unshmoopy question you'll find on the exam...

00:06

Which of the following is equivalent to negative 3 times one-half minus one-third times 2 to the fourth?

00:14

And here are the potential answers...

00:18

Lots of curveballs being thrown at your head here.

00:20

You can either panic... Or you can just break the problem into smaller

00:23

parts and solve 'em one by one. Like this.

00:26

So... powers are top priority -- even ahead of multiplication and division...

00:30

...so let's get rid of that 'to the 4th' thing first.

00:34

Two times two is 4 times 2 is 8 times 2 is 16...

00:38

...so 2 to the 4th is 16. Onward and upward.

00:41

Now we should factor in the negative 3 so we can get rid of this set of parentheses.

00:45

And if we distribute that ugly negative 3

00:47

we get negative 3 times a half is negative 3 over 2 ... minus ... negative 3 over 3.

00:53

Luckily 3 over 3 is the same as 1 over 1... and since we're subtracting a negative,

00:57

we're really just adding a positive 1. We want our denominators to be the same, so

01:02

we'll rewrite 1 as 2 over 2...

01:04

...and adding them together we now have negative 3 over 2 plus

01:07

2 over 2 equals... negative one-half.

01:11

Let's not forget our 16... we still have

01:13

to find the product of that and our negative one-half...

01:16

Negative one-half times 16 equals negative sixteen halves... or negative 8.

01:21

Looks like our final answer is negative 8... which is option A.

01:25

So much prettier than what we started with. It's like we got a makeover.

Full Transcript