Hey everyone! I'm having some trouble in algebra with simplifying expressions. I have a worksheet here with 20 expressions to simplify, and I'm struggling with most of them... I'm going to give 3 problems from the worksheet, and if someone could show me step by step how to simplify each one, that'd be great.
1.) (x^3*y^2)/(x^4*y)
2.) (x^4*y^4)/(x^-4*y^-4)
3.) [(x*y)/3]*(x*y)^-1
Let me know if you need clarification on any of the numbers or operations above (I'm not used to typing them out). So, yeah, if someone can show me how to do just those three step by step, I'm sure I'll be able to get the hang of it... Thanks!
1.) (x^3*y^2)/(x^4*y)
2.) (x^4*y^4)/(x^-4*y^-4)
3.) [(x*y)/3]*(x*y)^-1
Let me know if you need clarification on any of the numbers or operations above (I'm not used to typing them out). So, yeah, if someone can show me how to do just those three step by step, I'm sure I'll be able to get the hang of it... Thanks!
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1) imagine this in expanded form.
(x*x*x*y*y)
--------------------
(x*x*x*x*y)
Now x/x is 1 and y/y is 1, so cancel three x, and 1 y
Leaving y/x
So if there are more x on bottom, the leftovers will stay on bottom after canceling.
2) here it is easier to use the rule x^a/x^b= x^(a-b)
(x^4y^4)/(x^-4*y^-4)= x^(4--4)* y^(4--4)= x^8* y^8
3)using two rules: x^1*x^-1=x^0=1
and (xy)^a=x^a*y^a
(xy/3)]*(xy)^-1= (x*y*x^-1*y*-1)/3=(x^0*y^0)/3=1/3
Hoping this helps!
(x*x*x*y*y)
--------------------
(x*x*x*x*y)
Now x/x is 1 and y/y is 1, so cancel three x, and 1 y
Leaving y/x
So if there are more x on bottom, the leftovers will stay on bottom after canceling.
2) here it is easier to use the rule x^a/x^b= x^(a-b)
(x^4y^4)/(x^-4*y^-4)= x^(4--4)* y^(4--4)= x^8* y^8
3)using two rules: x^1*x^-1=x^0=1
and (xy)^a=x^a*y^a
(xy/3)]*(xy)^-1= (x*y*x^-1*y*-1)/3=(x^0*y^0)/3=1/3
Hoping this helps!