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Course: Class 7 (ICSE basics) > Unit 4
Lesson 2: Exponent properties- part 1/2Exponent properties 1
When multiplying numbers with common base, add exponents. Created by Sal Khan and Monterey Institute for Technology and Education.
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Why do we need exponets(33 votes)
Where else would nets get to attend expos? Sorry, I couldn't help myself.
Yes, exponents are a "shorthand" way of writing really big numbers, similar to scientific notation. It also helps with the actual operations, which one is easier to solve
50 x 1000000000 =
or
50 x 10^9 =
(actually the second one is scientific notation)(13 votes)
What if you wanted to divide numbers with exponents? What would you do?(9 votes)
Sal does a video on that. It's called: "Exponent Properties Involving Quotients." Hope it helps! If not, sorry :((2 votes)
At0:40, I don't see why it's reasonable to add the powers(5 votes)
what is the answer of (1/x)to the 0 power(3 votes)
If x is 0, the answer would be undefined, as 0/0 is undefined. However, anything else and the answer is 1.(2 votes)
in2:20sal writes like this...................
3(a^1*a^7)
but 7*1=7
where does sal get 8 from?(4 votes)
That is not correct, in the equation 3a (a^5) (a^2) we have 3 "a"s being multiplied with a^5 and a^2. The 3 "a"s are not the same as the "a"s that are raised to exponents because 3a is 3*a and a^5 is a*a*a*a*a To solve this, we would consolidate the exponentiated "a"s to get a^7 (a*a*a*a*a*a*a) times 3a (3*a) we would then expand this to make it easier to understand, getting us 3*a*a*a*a*a*a*a*a which is 3*a^8(0 votes)
What if there's a exponent outside the parenthesis?(2 votes)- Then you multiply everything inside the parenthesis. Check out the previous video titled Exponent properties with parentheses.(1 vote)
- how can you multiply an exponent? how can you multiply it?(2 votes)
So, for example, if I see:
a^5/2a-5
and I move the -5 up, the "a" goes with the -5, but the 2 doesn't.
Is that correct?(2 votes)
Isn't square roots to easy to memorize in a lot of people's minds. Because in the discussion area it seems like you could do this without exponents.(1 vote)
It is easy to memorize only in the very simple cases that you have at an introductory level. You will get to more complex problems where you will need to have mastered these exponent properties.
So, even though you might know an easier way to do the problem, you need to learn the techniques being taught so that when you get to the more difficult problems that the easy methods won't work for, you will have already learned the techniques that will work.(1 vote)
What's the formula for x^3 -8. I know it, I just can't remember it exactly(1 vote)- Can you clarify your question? Do you mean x raised to the (3-8) power? Or do you mean x raised to the third power - 8? Or something else?(1 vote)
0:40Video transcript
Simplify 3a times a to
the fifth times a squared. So the exponent
property we can use here is if we have the same
base, in this case, it's a. If we have it raised
to the x power, we're multiplying it
by a to the y power, then this is just going to
be equal to a to the x plus y power. And we'll think about why
that works in a second. So let's just apply it here. Let's start with the a to
the fifth times a squared. So if we just apply
this property over here, this will result in a to
the fifth plus two-th power. So that's what those guys
reduce to, or simplify to. And of course, we still
have the 3a out front. Now what I want to do is
take a little bit of an aside and realize why this worked. Let's think about what a to the
fifth times a squared means. A to the fifth
literally means a times a times a times a times a. Now, a squared literally
means a times a. And we're multiplying
the two times each other. So we're multiplying these
five a's times these two a's. And what have we just done? We're multiplying a
times itself five times, and then another two times. We are multiplying
a times itself. So let me make it clear. This over here is
a to the fifth. This over here is a squared. When you multiply
the two, you're multiplying a by itself
itself seven times. 5 plus 2. So this is a to the seventh
power. a to the 5 plus 2 power. So this simplifies to 3a
times a to the seventh power. Now you might say, how do I
apply the property over here? What is the exponent on the a? And remember, if I just
have an a over here, this is equivalent to
a to the first power. So I can rewrite 3a is 3
times a to the first power. And now it maybe makes
it a little bit clearer. A to the first power-- and
the association property of multiplication, I can
do the multiplication of the a's before I
worry about the 3's. So I can multiply
these two guys first. So a to the first times
a to the seventh-- I just have to add the exponents
because I have the same base and I'm taking the
product-- that's going to be a to
the eighth power. And I still have
this 3 out front. So 3a times a to
the fifth times a squared simplifies to
3a to the eighth power.