SOLUTION: Simplify (-3a^3b^2)(4ab)/ 2a^7b in at least TWO ways. Explain each step. Please help me with this and can you add the steps because they will help me figure out what I am doing w

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Simplify (-3a^3b^2)(4ab)/ 2a^7b in at least TWO ways. Explain each step. Please help me with this and can you add the steps because they will help me figure out what I am doing w      Log On


   



Question 1014033: Simplify (-3a^3b^2)(4ab)/ 2a^7b in at least TWO ways. Explain each step.
Please help me with this and can you add the steps because they will help me figure out what I am doing wrong.

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify (-3a^3b^2)(4ab)/ 2a^7b in at least TWO ways. Explain each step.
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1st:: [-3a^3b^2*4ab]/(2a^7b)
---
= [-12a^4b^3]/(2a^7b)
----
= -6b^2/a^3
==========
2nd:: (-3a^3b^2)
------
= -3a^3b^2
------
= -6b^2/a^3
=====
Cheers,
Stan H.
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Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Method 1: By writing the exponents as repeated multiplications,
breaking 4 into prime factors and cancelling:


%28-3%2Aa%5E3%2Ab%5E2%29%284%2Aa%2Ab%29%2F+%282%2Aa%5E7%2Ab%29

%28-3%2Aa%2Aa%2Aa%2Ab%2Ab%29%282%2A2%2Aa%2Ab%29%2F+%282%2Aa%2Aa%2Aa%2Aa%2Aa%2Aa%2Aa%2Ab%29




%28-3%2Ab%29%282%2Ab%29%2F+%28a%2Aa%2Aa%29

-%286b%5E2%29%2Fa%5E3

----------------------------------------------------------------


Method 2: By adding exponents to multiply and then subtracting
exponents to divide:

%28-3%2Aa%5E3%2Ab%5E2%29%284%2Aa%2Ab%29%2F+%282%2Aa%5E7%2Ab%29

%28-12%2Aa%5E4%2Ab%5E3%29%2F+%282%2Aa%5E7%2Ab%29

Divide the -12 on the top by the 2 on the bottom, getting -6 on the
top.

Subtract the exponents of "a", 7-4 getting exponent 3 and putting 
a3 on the bottom because the larger exponent of "a" was 
on the bottom.

Subtract the exponents of "b", 3-1 (understood) getting exponent 2 
and putting b2 on the top because the larger exponent of 
"b" was on the top. 

-%286b%5E2%29%2Fa%5E3

Edwin