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

$3^2\times x^{9\times2}\times3^4\times x^{2\times4}=3^2\times x^{18}\times3^4\times x^8$

Step2: Collect like terms

$3^2\times3^4\times x^{18}\times x^8$

Step 3: Simplify by using exponents laws

$3^{2+4}\times x^{18+8}=3^6\times x^{26}$

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

$(a^b)^c=a^{b\times c}$

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