Question

Explain why the exponents cannot be added in the product 12 to the power of three times 11 to the power of 3

Answer 1

Normally, we could add exponents.
however, that only is possible when the bases are the same
recall what exponents mean

12³=12*12*12


so we cannot add exponents for 12³*11³ because that means 12*12*12*11*11*11
it would not equal 12⁶ or 11⁶



or you  could refer to the rule
$(x^a)(x^b)=x^{a+b}$
notice when x=x then we can add the bases


fun fact below
we can reverse a previous exponential rule like this
since $(ab)^c=(a^c)(b^c)$ then $(a^c)(b^c)=(ab)^c$
therefor
$12^3*11^3=(12*11)^3$



we can't add the exponents because the bases are not the same