Question 1

Why is it 1 if the exponent is 0?

Accepted Answer

The zero exponent is equal to 1 to satisfy a certain case in manipulating bases with exponents. When multiplying or dividing the same base with exponents we add or subtract the exponents:

To find the value of (3^3)(3^2) [the short form of (3 X 3 X 3) X (3 X 3) or (27)(9)] we add exponents to get 3^(3+2) or 3^5 with a value of 243.

To find the value of (3^3)/(3^2)[the short form of (3X3X3)/(3X3) or 27/9] we subtract exponents to get 3^(3-2) or 3^1 with a value of 3.

Now let us consider the case in which the two exponents are the same:

To find the value of (3^3)/(3^3) [the short form of (3X3X3)/(3X3X3) or 27/27 we subtract exponents to get 3^(3-3) or 3^0 whose value must equal the value of 27/27, or 1. To make the equation true 3^0 must equal 1.

The general case is: (x^a)/(x^b)=x^(a-b). When b=a, by substitution, this becomes (x^a)/(x^a)=x^(a-a)=x^0. Now let’s consider it another way. On the left side of the equation we have a division of the same numerator and denominator, which has a value of 1 (anything divided by itself equals 1). On the right side we have x^0. To make the equation true x^0 must equal 1.

Question 2

lets say that my problem is 6 to the 8th power. is there a quicker easier way than doing 6*6*6*6*6*6*6*6  but not memory?

Accepted Answer

Yes, there is.
What is 6 times 6? That's just 36, or 6^2.
36^4 is equal to 6^8.
Now, what is 36 times 36? That's 1296.
1296^2= 6^8
Now, we just have to multiply 1296 by itself.
The result is 1,679,616.

Question 3

I was practicing some problems about the  *Pythagorean Theorem* and started off with the basics.
I know how to solve this problem, but when I checked their method, they did a different kind of _simplification_  that I didn't understand.

I got to this point:
```
((17^2) - (8^2))
```
But, instead just simplifying the powers and subtracting directly, they did this:

```
((17^2) - (8^2)) = (17 + 8) * (17 - 8)
```

I know that their way is also right because we both got the same answer of *225*.

All I want to know is how they got from this:

```((17^2) - (8^2))
```
To this:
```(17 + 8) * (17 - 8)
```
Thanks so much for taking the time to read this, I _really_  appreciate it!

Accepted Answer

Oh I get what you mean, it's something we call *difference of squares* . Here's the fundamental principle used:
x^2 - y^2 = (x + y)(x - y)
In this case, x = 17 and y = 8, it's just something you can memorize to make life easier! 
It's one of the multiple ways you can factor a quadratic, it's also very commonly seen.
Hope this helped :)
Happy holidays!!

Question 4

How do you think about fractional or decimal exponents such as 
2^0.3 ?

Accepted Answer

You would convert it into a fraction(0.3 = 3/10)
Then take the numerator and raise the base to it(2^3)
And you would square the value to the denominator

10sqrt(2^3)

As you see its very complex and you'll learn this later on

Question 5

what is 0 to the 0th power?

Accepted Answer

It is undefined. Why? Think of it as a paradox:
When 0 is raised to any number, it is zero
When any number is raised to the power of 0, it is one
So when you put those two together, it just doesn't make sense
So that is why...
Hope this helps

Question 6

At 0:16 why are there so many sixes? I'm confused.

Accepted Answer

Dear carla.
Those 6.6.6 represents 6X6X6. (multiplication between two numbers can also be denoted with "." instead of "X"). Please watch the video to completely understand about exponents

Algebra basics

Course: Algebra basics > Unit 1

Exponent example 2

Want to join the conversation?

Video transcript