Question

PLEASE HELP?

Compare and contrast, in complete sentences, the difference between the products of y2y5 and (y2)5. Provide the expanded form and product of each.

Answer 1

do you mean these two: \(\large y^2y^5 \) and \(\large (y^2)^5 \) ???

Answer 2

Yes :) @dpaInc

Answer 3

ok..
what does \(\large y^2 =\) ???

Answer 4

similarly, \(\large y^5 = \) ????

Answer 5

I don't know... @dpaInc

Answer 6

what does \(\large y\cdot y= \) ???

Answer 7

y^2?

Answer 8

ok... ill give you the first one... \(\large y^2 = y\cdot y \)
so \(\large y^5 = y\cdot y\cdot y\cdot y\cdot y \)
still with me?
your answer is correct in the post just above this one....

Answer 9

Yeah i'm with you

Answer 10

so,
\(\large y^2y^5 = \color {red}{y^2}\cdot \color {blue}{y^5} = \color {red}{y\cdot y}\cdot \color {blue}{y\cdot y\cdot y\cdot y\cdot y} = y^7 \)

Answer 11

now let's do \(\large (y^2)^5 \)

Answer 12

So that is the extended version of the first one?

Answer 13

yes...^^^

Answer 14

okay i got it

Answer 15

so for the second one..

Answer 16

\(\large (y^2)^5 =(y^2)\cdot (y^2)\cdot (y^2)\cdot (y^2)\cdot (y^2)\)
can you expand what's in each of those parenthesis?

Answer 17

ok...

Answer 18

(y^2)^5 = (y times y) (y times y) (y times y) (y times y) (y times y)

Answer 19

yes....
so using exponents, what does (y^2)^5 = ???

Answer 20

So for both of them i got

(y^2)^5 = y^2 * y^2 * y^2 * y^2 * y^2
y^2y^5 = y^2 * y^5 = y * y * y * y * y = y^7

Answer 21

what would the product of the 2nd one be?

Answer 22

(y^2)^5 = y^2 * y^2 * y^2 * y^2 * y^2 = y * y * y * y * y * y * y * y * y * y = y^10

Answer 23

I have to compare and contrast them as well

Answer 24

the purpose ( i think) of this problem is to show you a very important property of exponents...

\(\large y^2y^5=y^{2+5}=y^7\)
\(\large (y^2)^5=y^{2\cdot 5}=y^{10}\)

Answer 25

Okay i think i got it all, thank you so much @dpaInc ill have more questions in a few :)

Answer 26

yw...