Question: 2 and 3 with Exponent 7

Comment on 2 and 3 with Exponent 7

Why does it become 3*3 to the

Why does it become 3*3 to the power of 7? Thanks

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

Okay I get it now. Thank you

Great video. After viewing

Great video. After viewing this, I know how to answer a question I just got wrong on a practice test. Keep up the good work!

Why can’t it be (9^7)(4^7)? I

Why can’t it be (9^7)(4^7)? I understand your answer but I started out doing it wrong on my own.

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

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

That makes sense! Thanks! Now I think about it, I was doing one of the common mistakes. I’ll go and review those again.

Thanks again!

Is there no other way of

Is there no other way of solving this question? This method confuses me.

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,

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