Substitution and laws of exponents

crappiefisher26

New member
the example says this:

Use the substitution zy=x to express

x to the 5 / z to the 3y to the 3 as a power of x.

Using laws of exponents, we obtain

xto the 5/ z to the 3y to the 3= x to the 5/ (zy) to the 3

If we then use the substitution zy=x we have

x to the 5/(zy) to the 3= x to the 5/ x to the 3

that equals= x to the 2. howd they get the 2?

heres the question im stuck on

x to the 7y to the 7/z, z=xy

stapel

Super Moderator
Staff member
crappiefisher26 said:
x to the 5 / z to the 3y to the 3
Is this "x<sup>5</sup> / (z<sup>3y</sup>)<sup>3</sup>", or something else?

crappiefisher26 said:
xto the 5/ z to the 3y to the 3= x to the 5/ (zy) to the 3
If you are supposed to replace "x" with "zy" (or vice versa), then why have you replaced "z<sup>3y</sup>" with "zy"? (My confusion may stem from my earlier question regarding what, exactly, the expression is meant to be.)

Thank you.

Eliz.

Denis

Senior Member
Crappy, if you continue posting in that manner, nobody will be
fractions and powers PROPERLY.

For instance, 4 divided by the (sum of a and b) to the power x
should be posted like this: 4 / (a + b)^x

crappiefisher26

New member
ok well why didnt u tell me that earlier, so i ddnt have to sit here and fricken struggle

Denis

Senior Member
Did you not see the button "Forum Help" at top?

AND the "read before posting" note by Ted?

crappiefisher26

New member
Sorry. Heres the equation

x^7y^7/z=xy

Denis

Senior Member
crappiefisher26 said:
Sorry. Heres the equation
x^7y^7/z=xy
Ok, that's well done, Crappy:
x to the power 7 times y to the power 7 divided by z equals x times y.

but WHAT are you suppose to do with it?

As example, you can rearrange it like this: x^7y^7 / xy = z
then you can simplify that a bit: x^6y^6 = z or (xy)^6 = z

crappiefisher26

New member
No. Sorry i had a typing error. it should be

(x^7y^7/z), z=xy

it says using the given subsitution rewrite the expression in terms of one variable and simplify.

heres an example

(y^3z^3/x^3), x=yz

(y^3z^3/x^3)=(yz)^3

(yz)^3/(x^3)= x^3/x^3

skeeter

Senior Member
crappiefisher26 said:
No. Sorry i had a typing error. it should be

(x^7y^7/z), z=xy

x<sup>7</sup>y<sup>7</sup>/z = (xy)<sup>7</sup>/z = z<sup>7</sup>/z = ?(you finish)

it says using the given subsitution rewrite the expression in terms of one variable and simplify.

heres an example

(y^3z^3/x^3), x=yz

(y^3z^3/x^3)=(yz)^3

(yz)^3/(x^3)= x^3/x^3