To simplify
[tex](3x^9)^2(3x^2)^4[/tex]
First of all, Octavia error can be spotted from the correct steps below
Step1: Expand the expression
[tex]3^2\times x^{9\times2}\times3^4\times x^{2\times4}=3^2\times x^{18}\times3^4\times x^8[/tex]
Step2: Collect like terms
[tex]3^2\times3^4\times x^{18}\times x^8[/tex]
Step 3: Simplify by using exponents laws
[tex]3^{2+4}\times x^{18+8}=3^6\times x^{26}[/tex]
Step 4: Combine the terms.
The value is
[tex]729x^{26}[/tex]
Her error was that she didn't apply the exponents' law properly.
One of the laws she violated was
[tex](a^b)^c=a^{b\times c}[/tex]
Her mistake was that she did
[tex](a^b)^c=a^{b+c}\text{ which is wrong}[/tex]
So she missed it from our step 1 above
