Question

The value of 99 is to the power 2 98 pow2

Answer 1

Step-by-step explanation:

The unit digit of the following expression

is

Notice the Unit's digit in factorial of the numbers given below:

From the table, it can be observed that the (i.e., as Unit's digit).

This is due to the fact that factorial contains which places a zero at the result.

However the number of Zeroes placed at the result depends on the power of 2 or 5 .

To find the unit digit, the in the expression are considered, as these are the unit's digit contributing numbers.

The Numbers in rest of expression doesn't contribute to Unit's digit.

So, is

———[1]

Here, z is the last digit of the base.

Divide n by 4 and Note the Remainder

If

Check if z is even/odd

z =

If

Unit's digit is z itself.

If

Unit digit = Unit digit in

If

Unit digit = Unit digit in

If z = 5 ; then last digit in the product is also 5.

There is no need to check any case if z=5.

Find Unit's digit in

Unit's digit in = 1 ———[2]

Find Unit's digit in

Remainder when 98 divided by 4 is 2.

Unit's digit in ———[3]

Find the Unit's digit in

Remainder when 97 divided by 4 = 1

Unit's digit in ———[4]

Find the Unit's digit in

Remainder when 96 divided by 4 = 0

24 is an Even.

Unit's digit in ———[5]

Substituting [2], [3], [4], [5] in [1]

Required Unit's digit = Unit digit(Sum of Unit's digit in [1])

Required Unit's digit = Unit digit(1 + 4 + 6 + 6 + 0)

Required Unit's digit = Unit's digit (17)

Required Unit's digit = 7.

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Answer 2

⠀⠀⠀⠀⠀⠀$\huge{ \underline{ \purple{ \bold{ \underline{ \mathrm{AnS{\blue{weR }}}}}}}}$

99²=9801

98²=9604

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