Someone please help me with this math problem.?

Question

It says simplify, but, please help with these questions

1.(4xy^2)(5x^-3 y^-3)

2.(-5x^2yz^3)^3

3.3x^2 y^4 /18x^-2 y^2

and yes this is homework, but I could spend an hour looking for the answer in the book or someone could just show me how to do do the answer and save me an hour.

Answer 1

1)  

Multiply the numerical coefficients together then proceed and multiply the variables. It will help to rewrite the algebraic expression so that similar variables are together:

(4xy^2)(5x^-3 y^-3) = (4*5)   (x*x^3)  (y^2 * y^3)  

                            = 20  x^4  y^5     ----> same base, add exponents  

2)

(-5x^2yz^3)^3  =  (-5)^3  (x^2)^3  (y^3)  (z^3)^3    

                         =  -125 x^6 y^3 z^9      ---> Power of a Power, you multiply the exponents.

3)

3x^2 y^4 /18x^-2 y^2 =  (3/18) (x^2/x^2) (y^4/y^2)

                              =  (1/6)  (1)  (y^2)

                              =  (1/6) y^2  

                              =  (y^2)/6

                              

Answer 2

1.(4xy^2) + (5x^-3 y^-3)

=20x^-2 + y^-1

=1/(20x^2 + y)

2.(-5x^2yz^3)^3

=-125x^6y^3z^9

3.3x^2 y^4 /18x^-2 y^2

Is this: 3x^2+y^4 /18x^-2+y^2?

3x^2 + y^4

---------------

18x^-2 + y^2

x^4 + y^2

-------------

......6

OR. 3x^2y^4 /18x^-2y^2

3x^2y^4

-----------

18x^-2y^2

x^4y^2

----------

......6

Answer 3

Are the spaces in the equations, + signs?

2. when exponents are raised to an exponent, you multiply the exponents so

(-5x^2yz^3)^3 = -75 x^6 y^3 z^9 (spaces just so it reads easier)

Assuming they are plus signs, for the first eq, you multiply 4xy^2 times 5x^3 and y^-3.  When you multiply variables with exponents, you ADD the exponents.

For 3, when you divide variables with exponents, you subtract the exponents.