Determine the last digit of the expression $((48293)^{145!}) * ((25684)^{89!})$

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Official Explanation

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To find the last digit of the expression

((48293)^{145!}) * ((25684)^{89!})

, we first look at the last digits of the bases. The last digit of 48293 is 3, and the last digit of 25684 is 4. We need to find the last digit of

(3^{145!})

and

(4^{89!})

. The last digit of powers of 3 cycles through 3, 9, 7, 1, and since

145!

is very…

Comments

NafisFeb 13, 2025

thanks for posting

MaryamJun 21, 2024

Thank for sharing!

PranavJul 31, 2024

pls explain more?

What this question tests

Your grasp of exponent rules — multiplying and dividing powers, power-of-a-power, and negative/zero exponents.

Adding exponents when multiplying bases that have the same exponent, or confusing (x^a)^b with x^(a·b).