How would you simplify the problem below?*?

Question

(-3x^3 y^5)^3
__________
(9x^2 y)^2

Answer 1

Simplify > [(-3x^3y^5)^3] / [(9x^2y)^2]

First: place the exponents to each term and variable in parenthesis > when you have a variable with an exponent & raised to another exponent, add the exponents...

[-3^3 x^(3*3) y^(5*3)] / [(9^2 x^(2*2) y^2)]

[(-3)(-3)(-3) x^9y^15] / [(9)(9) x^4y^2]

[(-3)(9)x^9y^15] / [81x^4y^2]

[- 27x^9y^15] / [81x^4y^2]

Sec: simplify the coefficients & variables...

(-27/81)(x^9/x^4)(y^15/y^2

= (- x^5y^13)/3

Answer 2

The numerator first...
(ab)^3= a^3*b^3, e.g. (2*3)^3= 2*2*2*3*3*3=8*27=216= 6^3
Also, (a^b)^c= a^bc, e.g. (2^3)^2= 2^6= 64= 8^2

(-3(x^3)y^5)^3= [-3(x^3)]^3 * (y^5)^3]
= (-3)^3 * (x^3)^3 * (y^5)^3
= -27 * x^9 * y^15
= -27(x^9)(y^15)

Now the denominator,

(9(x)^2*y)^2
= (9(x)^2)^2 * y^2
= 81*x^4 * y^2
= 81(x^4)(y^2)

Taking the quotient/ ratio of these gives:

-27(x^9)(y^15) / 81(x^4)(y^2)
= (-27/81)*{(x^9)/(x^4)}*[(y^15)/(y^2)]

Now we know that (x^a)/(x^b)= x^(a-b), e.g. 2^3/2^2=2^1

Therefore your answer is

(-1/3)*(x^5)*(y^13)

To check that this works, let x=5 and y=2
Our solution is (-1/3)*5*5*5*5*5*2*2*2*2*2*2*2*2*2*2*2*2*2
=(-1/3)*3125*8192=-8533333.33

The question would be
(-3*5*5*5*2*2*2*2*2)*(-3*5*5*5*2*2*2*2*2)*(-3*5*5*5*2*2*2*2*2)
__________
(9*5*5*2)*(9*5*5*2)
=- 1728000000000/202500= -8533333.3333, as above. I hope this numerical proof will aid your understanding of the algebra.

Answer 3

Everthing in the ()gets raised (multiply exponents)

(-3)^3 x^9 y^15
--------------------
9^2 x^4 y^2

-27x^9y^15
---------------
81x^4 y^2

- (x^5 y^13)
------------
3

Answer 4

(-3x^3 y^5)^3
= (-3)^3 (x^3)^3 (y^5)^3
= -27x^9 y^15

(9x^2 y)^2
= 9^2 (x^2)^2 y^2
= 81x^4 y^2

You have
-27x^9 y^15 / (81x^4 y^2)
= -x^5 y^13 / 3

Answer 5

Ok, seriously, 18 QUESTIONS IN THE LAST 5 HOURS?! Do your OWN freaking homework! People like you tick me off. You can't expect people to just do your homework for you the rest of your life, can you? If you really need this much help, go ask your teacher. Jeez!

Answer 6

- x^5 y^13
-------------
12
Unless I misplaced something.

Answer 7

Erase it.