Need help bad with my Algebra 2 class

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juliecook77

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Dec 6, 2009
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Okay I am trying so hard to understand this math but it just feels so impssible. The more I try and understand it, the more I get frustrated. Here is the question:

-5y^4(y^5)^2/15y^7(y^2)^3

(3y^8)^4/(2zy^2)^4
 
ok I went to that link but I do not understand how they are working the problem. I want & need to understand this. Thank you though so much, I really appreciate it.
 
-5y^4(y^5)^2 / (15y^7(y^2)^3) : extra brackets required

rule1: a^x a^y = a^(x+y)
rule2: (a^x)^y = a^(xy)
rule3: a^x / a^y = a^(x-y)

Step1: simplify 5/15 = 1/3:
-y^4(y^5)^2 / (3y^7(y^2)^3)

Step2: rule2:
-y^4 y^10 / (3y^7 y^6)

Step3: rule1:
-y^14 / (3y^13)

Step4: rule3:
-y / 3

Kapish?

Your 2nd one will work similarly...let's see what you can do :wink:
 
The solving of this is easy if you understand how to combine the indices (powers or exponents).

2(3) is 3+3 or 2+2+2, 3 times 2 or 2 times 3 (3 two times... or 2 three times).
Multiplication is "successive addition".
The multiplier denotes the number of twos added together.

(2)(2)(2) is 2 times 2 times 2, 2 multiplied by itself twice, 3 twos in a row multiplied together.
This is written 2[sup:1jtgfi97]3[/sup:1jtgfi97].
The index denotes the number of twos in a row multiplied together.

Hence... 3[sup:1jtgfi97]4[/sup:1jtgfi97] is a short way to write (3)(3)(3)(3)
but 3[sup:1jtgfi97]4[/sup:1jtgfi97] is not 4[sup:1jtgfi97]3[/sup:1jtgfi97], unlike 3(4) = 4(3).

Hence x[sup:1jtgfi97]2[/sup:1jtgfi97]x[sup:1jtgfi97]3[/sup:1jtgfi97]=(x)(x)(x)(x)(x) = x[sup:1jtgfi97]5[/sup:1jtgfi97]
so multiplication of a number to one power by the same number to another power is simplified
by just adding the indices....x[sup:1jtgfi97]2[/sup:1jtgfi97]x[sup:1jtgfi97]3[/sup:1jtgfi97]=x[sup:1jtgfi97]2+3[/sup:1jtgfi97].

When dividing... 5[sup:1jtgfi97]7[/sup:1jtgfi97]/5[sup:1jtgfi97]4[/sup:1jtgfi97]=(5)(5)(5)(5)(5)(5)(5)/(5)(5)(5)(5).
4 fives under the line cancel with 4 fives above the line leaving 3 fives remaining.
When you divide, you may subtract the indices 5[sup:1jtgfi97]7[/sup:1jtgfi97]/5[sup:1jtgfi97]4[/sup:1jtgfi97]=5[sup:1jtgfi97]7-4[/sup:1jtgfi97]=5[sup:1jtgfi97]3[/sup:1jtgfi97]

You must be dealing with powers of the same numbers.

Hence x[sup:1jtgfi97]p[/sup:1jtgfi97]x[sup:1jtgfi97]q[/sup:1jtgfi97]=x[sup:1jtgfi97]p+q[/sup:1jtgfi97] and x[sup:1jtgfi97]p[/sup:1jtgfi97]/x[sup:1jtgfi97]q[/sup:1jtgfi97]=x[sup:1jtgfi97]p-q[/sup:1jtgfi97]

Also (x[sup:1jtgfi97]3[/sup:1jtgfi97])[sup:1jtgfi97]2[/sup:1jtgfi97]=x[sup:1jtgfi97]3[/sup:1jtgfi97]x[sup:1jtgfi97]3[/sup:1jtgfi97]

Try that logic on your problem
 
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