I have to simplify
(-x^5y^4)^4(3x^2y)^2(1/3xy)
I did
(x^20y^16)(9x^4y^2)(1/3xy)
(9x^24y^18)(1/3xy)
3x^25y^19
Is this correct?
Thank you for your help!
First of all, it's not a polynomial,as there is only one term.
It's ok to here:
(9x^24y^18)(1/3xy)
Now, is that 1/(3xy) or (1/3)xy ?
It appears that you meant (1/3) xy, but it's hard to say, since you some how got
(...)(1/3) = 3(...)
How did you manage to switch from dividing to multiplying by 3?
So, if you meant (1/3) xy, the answer is 1/3 3x^25y^19
If it was 1/(3xy), then you have
1/3 x^23y^17
In either case, you can't switch 1/3 to 3.
Now, if you meant
(...)/(1/3xy)
then you get a 3 in front, since you are dividing by 1/3.
Thank you for explaining my mistake.
To simplify the expression (-x^5y^4)^4(3x^2y)^2(1/3xy), we need to apply the properties of exponents and simplify each term separately before multiplying them together.
Let's start by simplifying each term:
1. Simplify (-x^5y^4)^4:
Applying the power of a power rule, we get (-x^5y^4)^4 = (-1)^4(x^5)^4(y^4)^4 = x^20y^16.
2. Simplify (3x^2y)^2:
Applying the power of a power rule, we get (3x^2y)^2 = (3)^2(x^2)^2(y)^2 = 9x^4y^2.
3. Simplify (1/3xy):
Since there's no exponent to simplify, we can leave it as it is.
Now, multiply all the simplified terms together:
(x^20y^16)(9x^4y^2)(1/3xy) = (x^20)(9x^4)(y^16)(y^2)(1/3)(x)(y) = (9/3)(x^(20+4))(y^(16+2))(1)(1) = 3x^24y^18.
Therefore, your simplified expression is 3x^24y^18.
So, your original result of 3x^25y^19 is incorrect. The correct simplified expression is 3x^24y^18.
Hope this helps! Let me know if you need further assistance.