Expert: Sherman D. - 11/21/2004

Question
Hi i am stuck on how to similfy the following equations. i would very much appreciate your help.

1.) 2z^3y^2  x  3z^2y  x  (1/4 zy)^-1

2.) 3^4  x  3^7  x  3^2

3.) (i cant type the symbol for pie so i'll use two blackslashs)
(\\17 - 1) (\\17 + 17)

4.) 1/(\\5 - \\3)

finally! 5.) (\\a  = \\4b)(\\a - \\b)

I appreciate you taking time out to help me as it will help complete any similiar questions I come across. Thankyou

Answer
1.)
2z^3y^2 * 3z^2y * ((1/4)zy)^-1
multiply the exponents, also when same variables with exponents are being multiplied, all you have to do is add them together, like this

((2 * 3) * z^(3 + 2) * y^(2 + 1)) * ((1/4)zy)^(-1)
6z^5y^3 * ((1/4)zy)^(-1)
becomes
6z^5y^3 * (1/((1/4)zy))
multiply across
(6z^5y^3)/((1/4)zy)
multiply the top half the the reciprical of (1/4)
((6 * 4)y^3z^5)/(zy)
(24y^3z^5)/(yz)
same as
(25y^3z^5)/(y^1z^1)
when identical variables with exponents are being divided, just subtract the exponents)
25 * y^(3 - 1) * z^(5 - 1)
25y^2z^4
By the way, i put the y in front of the z, just because alphabetically it is, but it doesn't matter how you but the variables as long as they are still being multiplied.

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2.)
3^4 * 3^7 * 3^2
since all the exponents have the same coefficient, you can just add the exponents and you get
3^(4 + 7 + 2)
3^13

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3.)
if by this you mean something like this
(17¶ - 1)(17¶ + 17)
Use the FOIL method and you get
(17¶ * 17¶) + (17¶ * 17) + (-1 * 17¶) + (-1 * 17)
becomes
289¶^2 + 289¶ - 17¶ - 17
becomes
289¶^2 + 272¶ - 17

By the way, the ¶ actually stands for paragraph when typing a letter. Its the only symbol that i know that comes close to pi.

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4.)
1/(5¶ - 3¶)
in this case you can treat ¶ like a variable, only we know the value of this variable.
1/((5 - 3)¶)
1/(2¶)
By the way, since ¶ is at the bottom, you can't write it like (1/2)¶, because then that would mean that the 1 and the ¶ were being multipled together, just in case you didn't know that.

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5.) If by this you mean
(a¶ + 4b¶)(a¶ - b¶)
a^2¶^2 - ab¶^2 + 4ab¶^2 - 4b^2¶^2
a^2¶^2 + 3ab¶^2 - 4b^2¶^2
since each ¶^2's don't have the same exact variable, you can't combine them.

IF BY \\ you actually meant square root instead, please let me know so i can correct my work.