Question

Find the last two digits of $\bf{2^{1000}}$ ​

Answer 1

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Step-by-step explanation:

To obtain the required last digit of 2^1000 :-

$2 {}^{1000} = (2 {}^{5} ) {}^{200} = (32) {}^{200}$

$⇒2 {}^{1000} = 2 {}^{200}$

$⇒2 {}^{1000} = 2 {}^{200} = (2 {}^{5}) {}^{8}$

$⇒2 {}^{1000} = 2 {}^{8}$

$⇒2 {}^{1000} = 256$

$⇒2 {}^{1000} = 6$

• Required last digit is 6

Answer 2

$\huge \purple\star \pink {answer} \huge \purple \star$

Step-by-step explanation:

To obtain the required last digit of 2^1000 :-

2¹⁰⁰⁰= (2⁵)²⁰⁰ = (32)²⁰⁰

⇒2¹⁰⁰⁰ = 2²⁰⁰

⇒2¹⁰⁰⁰ = 2²⁰⁰ = (2⁵)⁸

⇒2¹⁰⁰⁰ = 2⁸

⇒2¹⁰⁰⁰ = 256

⇒2¹⁰⁰⁰ = 6

• Required last digit is 6