Question

Conner and Jana are multiplying (3568)(39610).

Conner's Work Jana's Work
(3568)(39610) = 35 + 968 + 10 = 314618 (3568)(39610) = 35⋅968⋅10 = 345680
Is either of them correct? Explain your reasoning.

Answer 1

(edit: I researched this problem more, and it turns out this question is actually based on exponents. I will be deleting my previous reply.)

original problem:\[(3^{5}6^{8})(3^{9}6^{8})\]
Conner's work:\[(3^{5}6^{8})(3^{9}6^{8})\] = \[(3^{5+9}6^{8+10})\]=\[(3^{14}6^{18})\]

Jana's work:\[(3^{5}6^{8})(3^{9}6^{8})\] = \[(3^{5*9}6^{8*10})\]=\[(3^{45}6^{80})\]

Answer 2

for multiplying exponents with the same base, add the exponents

generic rule:
\[m^{a}*m^{b}=m^{a+b}\]

with this in mind, check both of their work again to see which one (if any) followed the rule correctly. keep careful track of bases and exponents.