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Multiplication of Monomials

Posted on 2011-02-24
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Last Modified: 2012-05-11
Evaluate each expression when a=2 and b=-3:

I am sorry I cannot type what's below as -a squared times b to the fourth power.

This is the equation:
-a exponent of 2 b exponent of 4

(-2)(-2)=4
(-3)(-3)(-3)(-3)=81
(4)(81)=324

The correct answer is -324

I don't really know what to do with the negative sign in front of the equation. (-a2ndb4th). Do I multiply (-) times both a2 and b4? Do I add it after I get the answer 324 as the last step? -324.

Thanks.
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Question by:kadin
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Expert Comment

by:mbkirk
ID: 34975888
So you mean (-a)^2 * b^4, where ^ means exponent?

The negative is applied to a, then squared.   So if a=2 and b = -3, it's 2*2+(-3)*(-3)*(-3)*(-3), or 324.

Now negate.  Gives you -324.

Think of it as

0-a^2*b^4

Powers, Parenthesis, Addition, Subtraction, Multiplication, Division.  

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Expert Comment

by:mbkirk
ID: 34975892
Sorry miswrote the first line - you meant "-(a^2)*(b^4) "- rest of my statement still holds.
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Author Comment

by:kadin
ID: 34975899
So when you say "Now negate". I take 324 and add the negative sign to it? -324
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Expert Comment

by:mbkirk
ID: 34975908
Right, because you've applied the exponents (first), now multiplication, then negation.

The leading -a is really 0-a.

Also ignore my "powers parenthesis" statement - guess it's the end of a long day.

Powers, Parenthesis, Multiplication,  Division, Addition,  Subtraction.

It's a standard order of operations you can apply here.  The leading "-a" is really saying "0-a", so by order of operations you apply that last to the result of the rest of the equation.

Fully parenthesized, it's 0-(a^2)*(b^4)
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Author Comment

by:kadin
ID: 34975936
Which one of these is the last operation in this case?

Powers, Parenthesis, Multiplication,  Division, Addition,  Subtraction.

It looks like your multiplying 0 or  - (a^2)*(b^4). I thought 0 times any number = 0. So 324 would end up as 0. Or are you just adding the - to the final number 324?
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Accepted Solution

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mbkirk earned 500 total points
ID: 34975942
0 is the leading subtraction.  saying "-a" by itself is really saying "0-a".  Since subtraction is the *last* thing you do in the order of operations and powers are the first, you'd do both powers, then the multiplication, then finally subtract the whole mess from 0.

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Author Comment

by:kadin
ID: 34975948
I see. The last step is -4 * 81 = -324.
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Author Closing Comment

by:kadin
ID: 34975957
Got it. Thanks for your help.
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Author Comment

by:kadin
ID: 34975962
Explaining order of operation was very enlightening.

Powers, Parenthesis, Multiplication,  Division, Addition,  Subtraction.
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Expert Comment

by:mbkirk
ID: 34976008
Sure, no problem.
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