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Octavia simplified the expression as shown explain octavia’s error and correct her work

Octavia simplified the expression as shown explain octavia’s error and correct her-example-1
User Akram
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1 Answer

22 votes
22 votes

To simplify


(3x^9)^2(3x^2)^4

First of all, Octavia error can be spotted from the correct steps below

Step1: Expand the expression


3^2* x^(9*2)*3^4* x^(2*4)=3^2* x^(18)*3^4* x^8

Step2: Collect like terms


3^2*3^4* x^(18)* x^8

Step 3: Simplify by using exponents laws


3^(2+4)* x^(18+8)=3^6* x^(26)

Step 4: Combine the terms.

The value is


729x^(26)

Her error was that she didn't apply the exponents' law properly.

One of the laws she violated was


(a^b)^c=a^(b* c)

Her mistake was that she did


(a^b)^c=a^(b+c)\text{ which is wrong}

So she missed it from our step 1 above

User ChosenJuan
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