Question

explain why the exponents cannot be added in the product 12 to the third power times 11 to the third power

Answer 1

The reason they cannot be added is because of 11 and 12. They are odd and even numbers and they have no link to each other. Because of this, you cannot add the exponents. 

Answer 2

Answer: Hi!

"the product 12 to the third power times 11 to the third power"

is equivalent to: $12^{3}*11^{3}$

You cant add the exponents because the numbers exponentiated are different (and they dont share any even factor) , this rule only applies when:

$x^{b} *x^{a} = x^{a + b}$

the only simplification you can make in this equation is:

$12^{3}*11^{3} = (12*11)^{3}$