The unit digit in the product (2467)^{153} ti | vedclass

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Question

(A) To find the unit digit of $(2467)^{153} 	imes (341)^{72}$,we look at the unit digits of the bases.$1$. For $(2467)^{153}$,the unit digit is the s

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(A) To find the unit digit of $(2467)^{153} 	imes (341)^{72}$,we look at the unit digits of the bases.$1$. For $(2467)^{153}$,the unit digit is the same as $7^{153}$.The powers of $7$ follow a cycle of $4$: $7^1=7, 7^2=49, 7^3=343, 7^4=2401$.Dividing the exponent $153$ by $4$,we get $153 = 4 	imes 38 + 1$. Thus,$7^{153}$ has the same unit digit as $7^1$,which is $7$.$2$. For $(341)^{72}$,the unit digit is the same as $1^{72}$.Since $1$ raised to any power is $1$,the unit digit is $1$.$3$. The unit digit of the product is the product of the unit digits: $7 	imes 1 = 7$.

The unit digit in the product $(2467)^{153} \times (341)^{72}$ is

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