Question

find the digit at the unit place of the number 7 power 219 * 3power 522​

Answer 1

The digit of the unit place of $7^{219}\times 3^{522}$ is 7\

Step-by-step explanation:

The Cyclic table for 7 is as follows:

$7^{1} =7\\\\7^{2} =49\\\\7^{3} =343\\\\7^{7} =2401$

Let’s divide 219 by 4 and the remainder is 3.

Thus, the last digit of $7^{219}$ is equal to the last digit of $7^{3}$ i.e. 3.

The Cyclic table for 3 is as follows:

$3^{1}=3\\\\3^{2}=9\\\\3^{3}=27\\\\3^{4}=81\\\\3^{5}=243$

Let’s divide 522 by 4, the remainder is 2. Hence the last digit will be 9.

Therefore, unit’s digit of $7^{219}\times 3^{522}$ is unit’s digit of product of digit at unit’s place of $7^{219}$  and  $3^{522}$ = 3 × 9 = 27.

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Answer 2

Answer:

that's

Step-by-step explanation:

The digit of the unit place of 7^{219}\times 3^{522}7

219

×3

522

is 7\

Step-by-step explanation:

The Cyclic table for 7 is as follows:

\begin{gathered}7^{1} =7\\\\7^{2} =49\\\\7^{3} =343\\\\7^{7} =2401\end{gathered}

7

1

=7

7

2

=49

7

3

=343

7

7

=2401

Let’s divide 219 by 4 and the remainder is 3.

Thus, the last digit of 7^{219}7

219

is equal to the last digit of 7^{3}7

3

i.e. 3.

The Cyclic table for 3 is as follows:

\begin{gathered}3^{1}=3\\\\3^{2}=9\\\\3^{3}=27\\\\3^{4}=81\\\\3^{5}=243\\\\\end{gathered}

3

1

=3

3

2

=9

3

3

=27

3

4

=81

3

5

=243

Let’s divide 522 by 4, the remainder is 2. Hence the last digit will be 9.

Therefore, unit’s digit of 7^{219}\times 3^{522}7

219

×3

522

is unit’s digit of product of digit at unit’s place of 7^{219}7

219

and 3^{522}3

522

= 3 × 9 = 27.

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