Question

Two students have bank accounts:
Sama: $ 4 3rd power ⋅ 4 −4th power /(4 2nd power)−5 power
Jimena: $ 3 ⋅ (3 8th power) 2nd power/(3 2nd power)3 ⋅ 3 0 power
Which person has the most money in their account?

They have the same amount of money
Jimena
Sama
You cannot compare the total amount because the bases are different.

Answer 1

Interpret the expressions as exponent laws and simplify.

Sama:
(4^3 · 4^(−4)) / (4^2)^(−5)
= 4^(3−4) / 4^(2·(−5))
= 4^(−1) / 4^(−10)
= 4^(−1+10) = 4^9 = 262,144.

Jimena:
3 · (3^8)^2 / (3^2)^3 · 3^0
= 3 · 3^(16) / 3^6 · 1
= 3^(1+16−6) = 3^11 = 177,147.

Since 262,144 > 177,147, Sama has the most money.