# 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