Simplify this question.
(3x^2)^3 (4y^2)^4 (3z^3)^2 devide (2x)^2 (9y^2)^3 (z)^4.
Thank you very much.
Please show detailed working step by step, in sequence so that I will understand.
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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