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.

This is a tricky question that Reina and Sam are multiplying (84) 5 (73) 9

and their work are

(84) 5 (73) 9 = 84 + 573 + 9 = 89712 Reina's

(84) 5 (73) 9 = 84⋅573⋅9 = 820727 Sam's

Actually they are doing or multiplying using exponents.

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 (8 ⁴) ⁵ (7 ³) ⁹ = 8 ⁴ˣ⁵ 7 ³ˣ⁹ = 8 ²⁰ 7 ²⁷

This is correct because Sam multiplied exponents correctly

Exponents are multiplied not added.