Unit Digit of Numbers in Exponential Form

Q.

Express 256 as a power of 4.

Q.

What is the last digit of $2^{100}$?

1. 2

2. 6

3. 4

4. 8

Q.

What are the last two digits of $7^{2008}$?

Q. Find the unit digit of the number ${99}^{123}.$

1. 9
2. 1
3. 8
4. 3

Q. Find the unit digit of the numeric expression: ${124}^{128}\times {126}^{124}$.

Q. Astronomy The table shows the mass of the planets, the sum and the moon in our solar system.

Celestial Body	Mass $\left(kg\right)$	Mass $\left(kg\right)$ Standard Notation
Sun	$1,990,000,000,000,000,000,000,000,000,000$	$1.99\times {10}^{30}$
Mercury	$330,000,000,000,000,000,000,000$
Venus	$4,870,000,000,000,000,000,000,000$
Earth	$5,970,000,000,000,000,000,000,000$
Mars	$642,000,000,000,000,000,000,000,000,000$
Jupiter	$1,900,000,000,000,000,000,000,000,000$
Saturn	$568,000,000,000,000,000,000,000,000$
Uranus	$86,800,000,000,000,000,000,000,000$
Neptune	$102,000,000,000,000,000,000,000,000$
Pluto	$12,700,000,000,000,000,000,000$
Moon	$73,500,000,000,000,000,000,000$

Which planet has about the same mass as earth?

Q. Astronomy The table shows the mass of the planets, the sum and the moon in our solar system.

Celestial Body	Mass $\left(kg\right)$	Mass $\left(kg\right)$ Standard Notation
Sun	$1,990,000,000,000,000,000,000,000,000,000$	$1.99\times {10}^{30}$
Mercury	$330,000,000,000,000,000,000,000$
Venus	$4,870,000,000,000,000,000,000,000$
Earth	$5,970,000,000,000,000,000,000,000$
Mars	$642,000,000,000,000,000,000,000,000,000$
Jupiter	$1,900,000,000,000,000,000,000,000,000$
Saturn	$568,000,000,000,000,000,000,000,000$
Uranus	$86,800,000,000,000,000,000,000,000$
Neptune	$102,000,000,000,000,000,000,000,000$
Pluto	$12,700,000,000,000,000,000,000$
Moon	$73,500,000,000,000,000,000,000$

Order the planets and the moon by mass, from least to greatest.

Q.

What is the last digit of $6^{109}$?

1. 3

2. 8

3. 6

4. 4

Q. What is the last digit of $8^{1026}$?

1. 4
2. 6
3. 8
4. 2

Q. Find the unit digit of 124¹²⁸ × 126¹²⁴.$\left[3\right]$

Q.

What is the last digit of $5^{209}$?

1. 4

2. 5

3. 6

4. 0

Q. The digit at unit's place in $(2^9{)}^{100}$ is

Q.

The digit in the units place in the product of$2x3x7x7x9$.

1. $9$

2. $7$

3. $6$

4. $3$

Q. Predict the ones digit, copy and complete this table and answer the question that follow.

$X$	$1^x$	$2^x$	$3^x$	$4^x$	$5^x$	$6^x$	$7^x$	$8^x$	$9^x$	${10}^x$
$1$	$1$	$2$
$2$	$1$	$4$
$3$	$1$	$8$
$4$	$1$	$16$
$5$	$1$	$32$
$6$	$1$	$64$
$7$	$1$	$128$
$8$	$1$	$256$
Ones Digits of the Powers	$1$	$2,4,8,6$

Predict the ones digit in the following:
${29}^{10}$

Q. Predict the ones digit, copy and complete this table and answer the question that follow.

$X$	$1^x$	$2^x$	$3^x$	$4^x$	$5^x$	$6^x$	$7^x$	$8^x$	$9^x$	${10}^x$
$1$	$1$	$2$
$2$	$1$	$4$
$3$	$1$	$8$
$4$	$1$	$16$
$5$	$1$	$32$
$6$	$1$	$64$
$7$	$1$	$128$
$8$	$1$	$256$
Ones Digits of the Powers	$1$	$2,4,8,6$

Predict the ones digit in the following:
$9^{20}$

Q. What is the last digit of $6^{100}$.

Q. Predict the ones digit, copy and complete this table and answer the question that follow.

$X$	$1^x$	$2^x$	$3^x$	$4^x$	$5^x$	$6^x$	$7^x$	$8^x$	$9^x$	${10}^x$
$1$	$1$	$2$
$2$	$1$	$4$
$3$	$1$	$8$
$4$	$1$	$16$
$5$	$1$	$32$
$6$	$1$	$64$
$7$	$1$	$128$
$8$	$1$	$256$
Ones Digits of the Powers	$1$	$2,4,8,6$

Describe patterns you see in the ones digit of the powers.

Q. If n is a natural number, then unit digit in $6^n-5^n$

1. $1$
2. $6$
3. $5$
4. $9$

Q. Unit digit of 10 x 15 x 18 = _____.

1. 5
2. 8
3. 0
4. 1