Reina and sam are multiplying (84)5 (73)9.

reina's work sam's work
(84)5 (73)9 = 84 + 573 + 9 = 89712 reina's
(84)5 (73)9 = 84⋅573⋅9 = 820727 sam's

is either of them correct? explain your reasoning.

Reina’s work (8⁴)₅(7³)⁹=8⁴⁺⁵+ 7³⁺⁹= 8⁹ 7¹²
This is incorrect  because she added exponents instead of multiplying exponents

Sams work (8⁴)⁵ (7³)⁹=8⁴ˣ⁵ 7³ˣ⁹= 8²⁰ 7²⁷
This is correct  because Sam multiplied exponents correctly

Exponents are multiplied not added.

Reina’s work (8⁴)₅(7³)⁹=8⁴⁺⁵+ 7³⁺⁹= 8⁹ 7¹²

This is incorrect  because she added exponents instead of multiplying exponents

Sams work (8⁴)⁵ (7³)⁹=8⁴ˣ⁵ 7³ˣ⁹= 8²⁰ 7²⁷

This is correct  because Sam multiplied exponents correctly

Exponents are multiplied not added.

Step-by-step explanation:

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.