Question: 2 and 3 with Exponent 7

Comment on 2 and 3 with Exponent 7

great!

Please kindly let me know how it got factor to :
(3 x 3^7)(2 x 2^7)
greenlight-admin's picture

Happy to help!

When it comes to combining terms involving VARIABLES, most students have no problem.

Consider the following examples:
d + d + d = 3d
r² + r² + r² = 3r²
√x + √x + √x = 3√x

Keep in mind that the variables d, r and x are represent numbers. So, we can apply the same technique to combining numbers.
For example:
11 + 11 + 11 = 3(11)
5² + 5² + 5² = 3(5²)
14.1 + 14.1 + 14.1 3(14.1)
Likewise, 3^7 + 3^7 + 3^7 = 3(3^7) = (3^1)(3^7) = 3^8

Similarly:
k + k = 2k
a³ + a³ = 2a³
√w + √w = 2√w
19 + 19 = 2(19)
5² + 5² = 2(5²)
7.8 + 7.8 = 2(7.8)
Likewise, 2^7 + 2^7 = 2(2^7) = (2^1)(2^7) = 2^8

Does that help?

Cheers,
Brent

Hi Brent,

I solved it in this way is it correct

(3)(3^7)(2)(2^7)

(6)(3^7)(2^7)
(6^1)(6^7)
= 6^8

Pls help
greenlight-admin's picture

Perfect approach!

This is a dumb question, but I need someone to tell me so I remember -- why doesn't 3^7+3^7+3^7 simplify to 9^7?
greenlight-admin's picture

An easy way to test whether your assumption is to test some smaller values.
For example, applying the same strategy, does 3^2 + 3^2 + 3^2 = 9^2?
Evaluate each part to get: 9 + 9 + 9 = 81
Doesn't work.

We can also say that 3^7 + 3^7 + 3^7 does not equal 9^7

Now let's find out what 3^7 + 3^7 + 3^7 DOES equal.

First some examples of an important property:
x + x + x = 3x
q² + q² + q² = 3q²
2k + 2k + 2k = 3(2k) = 6k

So, 3^7 + 3^7 + 3^7 = 3(3^7) = (3^1)(3^7) = 3^8
----------------------------

Having said all of that, the IS a rule that says: (a^c)(b^c) = (ab)^c
So, for example, (3^2)(3^2) = (9^2)
Likewise, (3^7)(3^7) = (9^7)
And (3^7)(3^7)(3^7) = (27^7)

Cheers,
Brent

Always Scan First!

Whenever you encounter a quantitative question with answer choices, be sure to SCAN the answer choices before performing any calculations. In many cases, the answer choices provide important clues regarding how to best solve the question. 

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