Question

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

Answer 1

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