Exponents And Powers Test

Result

Exponents And Powers Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

is equal to ______.

A
27

B
3⁵

C
297

D
3² + 3⁴

Solution

= 3⁴ + 3⁴ + 3⁴

= 3 x 3⁴

= 3⁵
Question 2
1 / -0

The value ofis

A

B

C

D

Solution

=

=

=

=
Question 3
1 / -0

Find the value of.

A
14456

B
16640

C
16679

D
17689

Solution

=

=

=

= 16640
Question 4
1 / -0

The value of (-11) x (-11) x (-11) x (-11) x (-11) + (-11) x (-11) x (-11) x (-11) x (-11) is

A

B

C

D

Solution

=

=
Question 5
1 / -0

If, then find the value of x.

A
1

B
2

C
3

D
4

Solution

-6 + x + 13 = 10

x + 7 = 10

x = 10 - 7

x = 3
Question 6
1 / -0

The value ofis

A
(xy)⁷

B
(xy)⁵

C
(xy)⁴

D
(xy)³

Solution

=

=

= (xy)⁷
Question 7
1 / -0

A

B

C

D

Solution

=

=

=

Question 8

1 / -0

Select the correct combination from the following:

	Exponent	Base	Value
A	4	4	256
B	3	9	81
C	3	5	225
D	5	2	16

A

B

C

D

Solution

A is correct.

4⁴= 4 x 4 x 4 x 4 = 256

Hence, base = 4

Value = 256

B = 9³ = 9 x 9 x 9 = 729

C = 5³ = 5 x 5 x 5 = 125

D = 2⁵= 2 x 2 x 2 x 2 x 2 = 32

Question 9
1 / -0

If, then the value of t is

A

B

C

D

Solution

-1 + 4t = 1

4t = 2

t =

t =
Question 10
1 / -0

Which among the following is equivalent to?

A
770

B
870

C
890

D
980

Solution

=

=

= 890
Question 11
1 / -0

If , then what is the value of x?

A
0

B
4

C
6

D
8

Solution

In division, when base is same, the powers are subtracted.
So, the powers will be subtracted while solving

Therefore, 7 - (x - 3) = 4
7 - x + 3 = 4
10 - x = 4
x = 6
Question 12
1 / -0

The number which is multiplied by (-6)^-1to getis

A

B

C

D

Solution

(-6)^-1=

=

Let the number it is to be multiplied by be x.

Then, according to question:
x x =

x =
Question 13
1 / -0

The value of is _______.

A

B

C

D

Solution

=

=

=
Question 14
1 / -0

Find the value of x^y+ y^x, if x = 7 and y = 3.

A
2510

B
2520

C
2530

D
2540

Solution

x^y+ y^x= 7³+ 3^{7

= 343 + 2187 = 2530}
Question 15
1 / -0

Find the value of .

A
-2187

B
-218.7

C
-21.87

D
-2.187

Solution

=

=

=

=

= -2.187
Question 16
1 / -0

In a hypothetical situation, there is an extremely large chocolate bar of area 4⁵ sq. cm. If we have to cut the chocolate in 2¹⁰ square equal pieces, then what will be the area of each piece?

A
1 sq. cm

B
2 sq. cm

C
4 sq. cm

D
None of the above

Solution

4⁵ = 1024 sq. cm
and, 2¹⁰ squares pieces = 1024 pieces
So, area of 1 piece = = 1 sq. cm
Question 17
1 / -0

A company's expense on petrol and food per employee in a month is Rs. 5000. If there are 2 × 10⁵employees in the company, then what is the total expense of the company on petrol and food per month?

A
Rs. 10 × 10⁹

B
Rs. 10 × 10⁸

C
Rs. 100 × 10¹⁰

D
Rs. 10 × 10¹⁰

Solution

Expense per employee = Rs. 5000 = Rs. 5 × 10³Total number of employees = 2 × 10⁵Total expense of the company per month = Rs. 5 × 10³× 2 × 10⁵= Rs. 10 × 10⁸
Question 18
1 / -0

The highest amount of money in the Reserve Bank in a certain year was approximately Rs. 3.7856 × 10²⁰ and the lowest amount of money in the bank the same year was approximately Rs. 2.8566 × 10²⁰. What was the average amount of money in the Reserve Bank that year?

A
Rs. 3.3211 × 10¹⁰

B
Rs. 3.3211 × 10²⁰

C
Rs. 3.3211 × 10⁴⁰

D
None of these

Solution

Highest amount of money = Rs. 3.7856 × 10²⁰
Lowest amount of money = Rs. 2.8566 × 10²⁰
Average amount of money = Rs. ((3.7856 + 2.8566 )× 10²⁰)÷ 2
= Rs. (6.6422 × 10²⁰ ÷ 2 )
= Rs. 3.3211 × 10²⁰
Question 19
1 / -0

The distance between the Earth and the Moon is 4 x 10⁵ km and the distance between the Earth and the Sun is 150 x 10⁶ km. Find the distance between the Moon and the Sun if all of them are in a straight line, given that Moon lies between the Earth and the Sun.

A
1496 x 10⁵km

B
1496 x 10⁴km

C
1496 x 10⁶km

D
None of the above

Solution

Moon lies between Earth and Sun. So, the distance

= 150 x 10⁶ - 4 x 10⁵ km

= 1500 x 10⁵ - 4 x 10⁵ km

= 1496 x 10⁵ km
Question 20
1 / -0

In a test, question 1 was = ?, and Amit's answer to it was 9^-9. Then, question 2 was = ?, and his answer was 125.

Which of the two questions did he answer correctly?

A
Only 1

B
Only 2

C
Both 1 and 2

D
Neither 1 nor 2

Solution

We know that a positive exponent under a numerator of 1 can be written as a negative exponent.

Therefore, = 9^-9
So, 1 is correct.
Now, = 5^-3=So, 2 is incorrect.

Therefore, he just got question 1 right.

Question 21

1 / -0

Match the following:

Column I	Column II
A. 7²+ 7⁵÷ 7³	I. 1.5
B. (-9)³÷ (-7)⁵	II. 2
C. (3⁰+ 3⁰+ 3⁰) ÷ (2⁰+ 2⁰)	III. 98
D.	IV.

A - II, B - IV, C - I, D - III

A - III, B - IV, C - I, D - II

A - I, B - II, C - III, D - IV

A - II, B - I, C - IV, D - III

Solution

A = 7²+ 7⁵÷ 7³
= 49 + 7²
= 49 + 49 = 98

B = (-9)³÷ (-7)⁵= -729 ÷ -16807

= C = (3⁰+ 3⁰+ 3⁰) ÷ (2⁰+ 2⁰)

= (1 + 1 + 1) ÷ (1 + 1)

= 3 ÷ 2 = 1.5

D =

= 1 + 1 = 2

Question 22
1 / -0

Fill in the banks with correct symbols:

A. ___ 5²⁵

B.___ 1

C. ___

A
A. =, B. =, C. =

B
A. >, B. =, C. <

C
A. =, B. =, C. <

D
A. =, B. <, C. >

Solution

A.
= 5²⁵B.
= 1³= 1

Therefore,= 1

C.

=
=
<

Therefore, < .
Question 23
1 / -0

Which of the following statements is/are true?

Statement I: If x = , then the value of x⁴- 3x²+ 2x = 216.

Statement II: If , then x = 3.

A
Only Statement I

B
Only Statement II

C
Both statements I and II

D
Neither statement I nor statement II

Solution

Statement I:

x = =

=> x = 4

Hence, x⁴- 3x²+ 2x = 216

L.H.S.

= 256 - 48 + 8 = 216

Statement II:

L.H.S

= 36 x 9 = 324

Using x = 3, solve R.H.S:

= 64

Hence, it is incorrect.

So, only statement I is correct.
Question 24
1 / -0

Which of the following statements are true?

(A) If p and q are non-zero rational numbers and n is a positive integer, then pⁿ qⁿ= .(B) Expanded form of 1.2 times 10¹⁰ = 12000000000
(C) 8² is smaller than 3⁵.
(D) The base and power in the expression (5 x 5)²are 5 and2, respectively.

A
A, B and C

B
B and C

C
B, C and D

D
All of them

Solution

A. If p and q are non-zero rational numbers and n is a positive integer,then pⁿ qⁿ= .
This is false. It will be equal to .
B. Expanded form of 1.2 times 10¹⁰= 12000000000. This is true.
C. 8²= 64
3⁵= 243
Therefore, C is true.
D. The base is 25 and power is 2 in (5 x 5)².
Therefore, D is false.
Question 25
1 / -0

Fill in the blanks:

1. The _____________ form is a way of expressing a standard number using a base and a smaller raised number called an exponent.

2. = __________

3. = ____________

A
standard, 4, 2

B
exponential, 4, 3

C
standard, 4, 3

D
exponential, 4, 2

Solution

The exponential form is a way of expressing a standard number using a base and a smaller raised number called an exponent.

= 1 + 1 + 6 ÷ 3 = 2 + 2 = 4

==== 3