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Comment on 2 and 3 with Exponent 7
Why does it become 3*3 to the
This is a general property of
This is a general property of all numbers.
Let's examine some similar examples:
8 + 8 + 8 = (3)(8)
1.1 + 1.1 + 1.1 = (3)(1.1)
20 + 20 + 20 = (3)(20)
x + x + x = 3x
k² + k² + k² = 3k²
Likewise, 3^7 + 3^7 + 3^7 = (3)(3^7)
Does that help?
Okay I get it now. Thank you
Great video. After viewing
Why can’t it be (9^7)(4^7)? I
You are suggesting that 3^7 +
You are suggesting that 3^7 + 3^7 + 3^7 = 9^7
So, you are adding the bases and keeping the exponents the same.
Unfortunately, this approach is not valid.
Let's examine some counter-examples that demonstrate that we can't just add the bases and keep the exponents the same:
1^5 + 1^5 + 1^5
Using your approach, we get: 1^5 + 1^5 + 1^5 = 3^5
Is this true?
No.
1^5 = 1
So, 1^5 + 1^5 + 1^5 = 1 + 1 + 1 = 3
However, your approach suggests that 1^5 + 1^5 + 1^5 = 3^5, yet 3^5 = 243
Or what about:
5^2 + 5^2
Using your approach, we get: 5^2 + 5^2 = 10^2
Is this true?
No.
5^2 = 25
So, 5^2 + 5^2 = 25 + 25 = 50
However, your approach suggests that 5^2 + 5^2 = 10^2 = 100
Does that help clear things up?
Cheers,
Brent
That makes sense! Thanks! Now
Thanks again!
Is there no other way of
Unfortunately, there's no
Unfortunately, there's no better approach.
This questions tests a very important general property of all numbers, so let's go over the solution.
First, here are some similar examples:
8 + 8 + 8 = (3)(8)
1.1 + 1.1 + 1.1 = (3)(1.1)
20 + 20 + 20 = (3)(20)
x + x + x = 3x
5w + 5w + 5w = (3)(5w) = 15w
k² + k² + k² = 3k²
Likewise, 3^7 + 3^7 + 3^7 = (3)(3^7)
The same concept applies to 2^7
Does that help?
Cheers,
Brent
Hi Brent,
Thank you for this video.
I have a slightly different approach, but I do not know if it's the right method
I factor out (3^7)(1+1+1) x (2^7)(1+1)
= (3^7)(3^1) x (2^7)(2^1)
= 3^8 x 2^8
= 6^8
Is my method valid?
Yours is a perfectly valid
Yours is a perfectly valid approach.
In my approach, I collected like terms to get: 3^7 + 3^7 + 3^7 = (3)(3^7), in the same way that k + k + k = 3k.
In your approach, you took 3^7 + 3^7 + 3^7 and factored out a 3^7 to get: 3^7(1 + 1 + 1)
When we simplify 3^7(1 + 1 + 1), we get (3)(3^7)
So, both approaches allow us to simplify 3^7 + 3^7 + 3^7 to get (3)(3^7)
Cheers,
Brent
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