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Mathematics 6 Online
OpenStudy (anonymous):

HELPPPP !!!!!!!!!!

OpenStudy (anonymous):

Below are two expressions. Simplify each and then choose the statement that is true.

OpenStudy (anonymous):

Expression #1 ---- > (3x^2)3x^2 Expression #2 -----> (3x^3)^2(x^2)

OpenStudy (anonymous):

answer choices The exponents in Expression #1 are greater than the exponents of Expression #2. The exponents on Expression #2 are greater than the exponents of Expression #1. The exponents of Expression #1 are the same as the exponents of Expression #2. The relationship cannot be determined with the given information.

jimthompson5910 (jim_thompson5910):

what do you get when you simplify (3x^2)3x^2

OpenStudy (anonymous):

I have no clue

jimthompson5910 (jim_thompson5910):

3*3 = ??

OpenStudy (anonymous):

9

jimthompson5910 (jim_thompson5910):

x^2 times x^2 = ???

OpenStudy (anonymous):

4

jimthompson5910 (jim_thompson5910):

not just 4

OpenStudy (anonymous):

???

jimthompson5910 (jim_thompson5910):

x^2 times x^2 is not 4

jimthompson5910 (jim_thompson5910):

but 4 is part of it

OpenStudy (anonymous):

x^4 ?

jimthompson5910 (jim_thompson5910):

good

jimthompson5910 (jim_thompson5910):

so (3x^2)3x^2 simplifies to 9x^4

OpenStudy (anonymous):

Ok but what statement is true ?

jimthompson5910 (jim_thompson5910):

now simplify (3x^3)^2(x^2)

OpenStudy (anonymous):

idk how to do that one

jimthompson5910 (jim_thompson5910):

(3x^3)^2 is the same as (3x^3)(3x^3) multiply that out first

OpenStudy (anonymous):

9x^6 ?

jimthompson5910 (jim_thompson5910):

good

jimthompson5910 (jim_thompson5910):

so (3x^3)^2(x^2) becomes (9x^6)(x^2)

jimthompson5910 (jim_thompson5910):

multiply that out

OpenStudy (anonymous):

18x^8 ?

jimthompson5910 (jim_thompson5910):

close, but no

OpenStudy (anonymous):

then idk

jimthompson5910 (jim_thompson5910):

(9x^6)(x^2) is the same as (9x^6)(1x^2) which becomes what?

OpenStudy (anonymous):

idk

jimthompson5910 (jim_thompson5910):

what are the coefficients

OpenStudy (anonymous):

9 ?

jimthompson5910 (jim_thompson5910):

and what else

OpenStudy (anonymous):

1 ?

jimthompson5910 (jim_thompson5910):

multiply them to get ???

OpenStudy (anonymous):

9 ?

jimthompson5910 (jim_thompson5910):

9 is the final coefficient

jimthompson5910 (jim_thompson5910):

now multiply x^6 and x^2

jimthompson5910 (jim_thompson5910):

you did that and got x^8 so the (9x^6)(x^2) simplifies to 9x^8

jimthompson5910 (jim_thompson5910):

we started with Expression #1 ---- > (3x^2)3x^2 Expression #2 -----> (3x^3)^2(x^2) they both simplify to Expression #1 ---- > 9x^4 Expression #2 -----> 9x^8

jimthompson5910 (jim_thompson5910):

now you just compare the exponents in the simplified expressions

OpenStudy (anonymous):

so it would be The exponents on Expression #2 are greater than the exponents of Expression #1 ?

jimthompson5910 (jim_thompson5910):

yep you got it

OpenStudy (anonymous):

thank you but one more

OpenStudy (anonymous):

Expression #1 -----> (3d)^3(d) Expression #2 -----> (3d^2)^2

jimthompson5910 (jim_thompson5910):

same idea really, just with difference expressions

jimthompson5910 (jim_thompson5910):

show me what you can do here

OpenStudy (anonymous):

So Expression #1 ------> 9d ?

jimthompson5910 (jim_thompson5910):

no

jimthompson5910 (jim_thompson5910):

(3d)^3 = 3^3 * d^3 = ???

OpenStudy (anonymous):

9d^3 ?

jimthompson5910 (jim_thompson5910):

3^3 is not 9 though

jimthompson5910 (jim_thompson5910):

3^3 = 3 cubed = ??

OpenStudy (anonymous):

27 ?

jimthompson5910 (jim_thompson5910):

(3d)^3(d) turns into (27d^3)(d)

jimthompson5910 (jim_thompson5910):

what does (27d^3)(d) become?

OpenStudy (anonymous):

27d^3 ?

jimthompson5910 (jim_thompson5910):

no

jimthompson5910 (jim_thompson5910):

think of (27d^3)(d) as (27d^3)(1d^1)

OpenStudy (anonymous):

that mean it would be the same

jimthompson5910 (jim_thompson5910):

no not quite

jimthompson5910 (jim_thompson5910):

27*1 = 27, yes that stays the same but something else changes

jimthompson5910 (jim_thompson5910):

d^3 * d^1 = ???

OpenStudy (anonymous):

d^4 ?

jimthompson5910 (jim_thompson5910):

yep

jimthompson5910 (jim_thompson5910):

(27d^3)(d) turns into 27d^4

jimthompson5910 (jim_thompson5910):

now simplify (3d^2)^2

OpenStudy (anonymous):

9d^4 ?

jimthompson5910 (jim_thompson5910):

good

jimthompson5910 (jim_thompson5910):

Expression #1 -----> (3d)^3(d) Expression #2 -----> (3d^2)^2 becomes Expression #1 -----> 27d^4 Expression #2 -----> 9d^4

OpenStudy (anonymous):

thank you ! Last question can you also help me simplify (3x^3y^4)^2

jimthompson5910 (jim_thompson5910):

how far did you get

OpenStudy (anonymous):

Ok so I tried working it out and got 9x^5y^6 ?

jimthompson5910 (jim_thompson5910):

good try, but no

jimthompson5910 (jim_thompson5910):

when you have (x^3)^2, you multiply the exponents to get x^(3*2) = x^6

jimthompson5910 (jim_thompson5910):

use that idea to simplify

OpenStudy (anonymous):

so 9x^6y^8 ?

jimthompson5910 (jim_thompson5910):

good

OpenStudy (anonymous):

so (3x^3y^4)^2 is simplified to 9x^6y^8

jimthompson5910 (jim_thompson5910):

yep that is correct

OpenStudy (anonymous):

thank you for your help !!!!!!!!!!

jimthompson5910 (jim_thompson5910):

you're welcome

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