Simplify the following Equations?

Question

(-2x^2)^3(4x^3)^-1 and (3x)^-2 (3x^2/2)^2

Answer 1

There is not an equation in sight!
An equation requires "=" sign.
These are expressions.
Expression 1
(- 2 x ²) ³ (4 x ³)^(-1)
(- 8) x^6 / (4 x ³)
( - 2 ) x ³

Expression 2
9 x^4 / [ (3 x) ² (4) ]
x ² / 4

Answer 2

Are these equations ?
(2x^2)^3 (4x^3)^-1
= 2x × 2x × 2x / 4 × x × x × x
= 2 x / x
= 2

(3x^-2)(3x^2/2)^2
= [3 / (x × x)] × [(3 x ^2× 3x^2)/ 2 × 2]
=3 × 3 × 3x^2 / 2 × 2
= 27x^2/4

If these are equations then
27x^2 /4 = 2
or x^2 = 8/27
or x = + or – under root 8/27
= + or – (2/3) × under root 2/3

Answer 3

(-2x^2)^3 * (4x^3)^-1

(-8x^6) x 1 / (4x^3)

-2x^3 <---- for first equation


2nd equation

(3x)^-2 * [(3x^2) / 2)]^2

[1 / (3x)^2] x [(3x^2) / 2)]^2

[ 1 / (9x^2) ] x [ (9/4)x^4 ]

(x^2) / 4

(x / 2)^2

Answer 4

Problem 1:

In this problem.... you have (4x^3)^-1.... that is the same as if you wrote it this way...

.... 1 ....
----------
(4x^3)

And (-2x^2)^3 is the same as (-2x^2)*(-2x^2)*(-2x^2) = -8x^6

So....

-8x^6
---------- = -2x^(6-3) = -2x^3
(4x^3)


Problem 2:

In this problem.... you have (3x)^-2.... that is the same as if you wrote it this way...

.... 1 ............. 1 ............. 1
---------- = ------------ = ---------
(3x)^2 ..... (3x)(3x) ..... 9x^2

And ([3x^2] / 2)^2 is the same as ([3x^2] / 2) * ([3x^2] / 2) = [9x^4 / 4]

So....



.. 1 ............. 9x^4
---------- x ------------ = ** 9's cancel out and you are left with **
9x^2 ............ 4

... x^4
= ------ = (1/4) x^(4-2) = (1/4) x^2
....4x^2

Answer 5

I like your method of making brains crack at your question.
These are not equations as there is no equal to sign.
Sorry for those who answered.

Answer 6

-2x and 27