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Question:Simplify this question.

(3x^2)^3 (4y^2)^4 (3z^3)^2 devide (2x)^2 (9y^2)^3 (z)^4.

Thank you very much.

Answers:
(3x^2)^3 is the same as (3 * x^2) * (3 * x^2) * (3 * x^2) =
= 27 * x^(2+2+2)= 27x^6

(4y^2)^4 is the same as (4 * y^2) * (4 * y^2) * (4 * y^2) * (4 * y^2) =
= 256 * y^(2+2+2+2) = 256y^8

(3z^3)^2 is the same as (3 * z^3) * (3 * z^3) = 9 * z^(3+3) = 9z^6

(2x)^2 is the same as (2 * x) * (2 * x) = 4 * x^(1+1) = 4x^2

(9y^2)^3 is the same as (9 * y^2) * (9 * y^2) * (9 * y^2) =
= 729 * y^(2+2+2) = 729y^6

(z)^4 is the same as z^4

so. now you right the problem again with the results that you find...

GIVEN: (3x^2)^3 (4y^2)^4 (3z^3)^2 divided by (2x)^2 (9y^2)^3 (z)^4

is the same as...

(27x^6)(256y^8)(9z^6) DIVIDED BY (4x^2)(729y^6)(z^4)

which can be written

(27x^6)(256y^8)(9z^6)
-----------------------------
(4x^2)(729y^6)(z^4)

1
X....64.....X
27x^6)(256y^8)(9z^6). 64 x^4 y^2 z^2
------------------------------... = ---------
(4x^2)(729y^6)(z^4)..3
....X
....27
.....X
.....3

64 x^4 y^2 z^2
-----------------
. 3


KEY MATH CONCEPTS YOU SHOULD KNOW:

(3y^2)^3 is the same as 3y^2 * 3y^2 * 3y^2 = 27 * y^(2+2+2) = 27y^6

or... you could have seen it this way...

(3y^2)^3 is the same as 3^3 * (y^2)^3 = 27 * y^(2*3) = 27y^6


When DIVIDING exponents... like

x^8
----
x^5

you SUBTRACT the exponents... so long as you have the same base. our base is "x"... so because the bases are the same... you can therefore subtract the exponents...

so...

x^8
---- = x^(8-5) = x^3
x^5

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