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Here’s an unshmoopy question you’ll find on the exam…
Simplify the expression (8)-3 × (16)2. And here are the potential answers:
How in the world do we take a negative exponent?
The process isn’t really that intuitive. Like… how can ya raise something to a NEGATIVE
power?
It’s like GIVING someone a bunch of taxes. Just doesn’t make natural sense.
Let’s start with the second part of this, which is easy…
…square 16… so 16 times 16 is 256. Done. Now we have to figure out how we negatively
cube 8. And we can’t just cube 8 with a bad attitude.
One thing that’ll help is to realize that anything to a negative exponent can be rewritten
as 1 OVER that number…
…that is, 8 to the negative 3rd power is the same as 1 over just a normal positive
8… cubed.
So the first part is just 1 over 512. Now we have 1 over 512 times 256… which
is 256 over 512… or just one half.
And our answer is B.