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Which expression is equivalent to (a^2b^4c)^2(6a^3b)(2c^5)^3/4a^6b^12c^3 ?

Please help, need answer fast! Which expression is equivalent to (a^2b^4c)^2(6a^3b-example-1
User Jmz
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2 Answers

4 votes
the answer is c. 12ac^14/b^3
Please help, need answer fast! Which expression is equivalent to (a^2b^4c)^2(6a^3b-example-1
User Pratheesh
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7 votes

Answer:

The correct answer is C


(12ac^(14))/(b^3)

Explanation:

We want to simplify


((a^2b^4c)^(2)(6a^3b)(2c^5)^3)/(4a^6b^(12)c^3).


Recall this property of exponents,


(a^m)^n=a^(mn)

When we apply this property our expression becomes,


=((a^4b^8c^2)(6a^3b)(2^3c^15))/(4a^6b^(12)c^3).

We rearrange to get


=(6*8* a^4* a^3 * b^8* b* c^2* c^(15))/(4a^6b^(12)c^3).


We now apply another property of exponents to simplify the numerator.

According to this property,


a^m* a^n=a^(m+n)

When we apply this property, the expression will now be,



=(6*8* a^(4+3) * b^(8+1) c^(2+15))/(4a^6b^(12)c^3)


This simplifies to,



=(48* a^(7) * b^(9) c^(17))/(4a^6b^(12)c^3)


We again apply this property of exponents,


(a^m)/(a^n)=a^(m-n).


When we apply this property, the expression will be,



=12* a^(7-6) * b^(9-12) c^(17-3)



=12* a^1 * b^(-3) c^(14)


We rewrite this as a positive index to get,



=(12ac^(14))/(b^3)


The correct answer is C



User Nu
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