Exponents And Powers Test

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Exponents And Powers Test - 6

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Weekly Quiz Competition

Question 1
1 / -0

3³ + 3³ + 3³ + 3³ + 3³is equal to

A
115

B
125

C
135

D
145

Solution

3³ + 3³ + 3³ + 3³ + 3³
= 5 x 3³
= 5 x 27
= 135
Question 2
1 / -0

The value of is

A
100

B
121

C
144

D
164

Solution
Question 3
1 / -0

What will come in place of question mark (?) in the following expression?

A

B

C

D

Solution

= ((6)² - (4)²) ÷ (7)²= ((36) - (16)) ÷ (49)

=
Question 4
1 / -0

What is the value of (3° + 5° + 4° × 3°) × 2²?

A
4

B
10

C
12

D
80

Solution

(3° + 5° + 4° × 3°) × 2²Using the law of exponents: (x)° = 1
= [1 + 1 + 1 × 1] × 2² 3 4 = 12
Question 5
1 / -0

If , then x is equal to

A
0

B
1

C
2

D
3

Solution

Base is same.
Therefore, powers will be equal.
12 + x = 15
x = 3
Question 6
1 / -0

The value of is

A

B

C

D

Solution

= m ^{(-5 + 4)} × n ^{(-4 + 5)}

=

=
Question 7
1 / -0

What will come in place of question mark (?) in the following expression?

= ?

A

B

C

D

Solution
Question 8
1 / -0

What is the value of 'x' if 10⁵×10^-3 = 10^x?

A
8

B
2

C
-2

D
-15

Solution

10⁵ × 10^-3 = 10^x
Adding the exponents, we get
10^{5 + (-3)} = 10^x
(10)² = (10)^x
As the bases are the same, the powers will be equal.
So, x = 2
Question 9
1 / -0

If , then the value of x is

A

B

C

D

Solution

=

Since base is same, powers will be equal.
-10 = -6 + 4x - 1
4x = -10 + 7
x = -
Question 10
1 / -0

Which of the following is equivalent to 8.9 × 10^-7?

A
0.0000000089

B
0.000000089

C
0.0000089

D
0.00000089

Solution

8.9 × 10^-7
=
= 0.00000089
Question 11
1 / -0

If , then n is equal to

A
3

B
4

C
5

D
6

Solution

Since base is same, powers must be equal.
n + 11 = 16
n = 16 - 11 = 5
n = 5
Question 12
1 / -0

The number which is multiplied by (-7)² to obtain a product equal to 35 is

A

B

C

D

Solution

Let the number be x.
Then,
(-7)² × x = 35
x = 35/49
x = 5/7
Question 13
1 / -0

The value of is

A

B

C

D

Solution

=
Question 14
1 / -0

The value of x⁴+ y⁶, if x = 7 and y = 3 is

A
3002

B
3303

C
3130

D
2938

Solution

x⁴ + y⁶
= 7⁴ + 3⁶
= 2401 + 729
= 3130
Question 15
1 / -0

The value of is

A

B

C

D

Solution
Question 16
1 / -0

A square shaped park has an area of 4¹⁹ sq.m. A gardener wants to make square flower beds of 16⁵ sq.m. How many flower beds can be made?

A
4⁹

B
16⁵

C
4¹⁹

D
None of these

Solution

Required number of beds =
=

= 4¹^9-10

= 4⁹
Question 17
1 / -0

A jeweller spends Rs. 90,000 on buying a gold block from a miner. If the jeweller has 2 x 10⁴blocks of gold, then find out the total money spent on gold by the jeweller.

A
Rs. 18 x 10⁹

B
Rs. 18 x

C
Rs. 18 x 10¹⁰

D
Rs. 18 x 10⁷

Solution

Total amount spent on gold
= 90000 (2 x 10⁴)
= Rs. 18 x 10⁸
Question 18
1 / -0

Two galaxies, Andromeda and Milky Way, revolve around each other. The longest distance from Andromeda to Milky Way is 5.236 x 10¹⁶light years and the shortest distance from Milky Way to Andromeda is 2.541 x 10¹⁶ light years. Find the average distance between the two galaxies.

A
3.5450 x 10¹⁶

B
3.8885 x 10¹⁶

C
3.4513 x 10¹⁶

D
3.8881 x 10³²

Solution

Longest distance = 5.236 x 10¹⁶
Shortest distance = 2.541 x 10¹⁶
Total distance = 5.236 x 10¹⁶ + 2.541 x 10¹⁶
= 7.777 x 10¹⁶
Average distance =
= 3.8885 x 10¹⁶
Question 19
1 / -0

Distance from Paris to Canada is 3.7 x 10⁸km and distance from Canada to England is 4.3 x 10⁷km. The distance from Paris to England in standard form is

A
4.13 x 10⁶km

B
4.13 x 10⁸km

C
5.23 x 10⁸km

D
None of these

Solution

Distance from Paris to Canada
= 3.7 x 10⁸km = 37,00,00,000 km
Distance from Canada to England
= 4.3 x 10⁷km = 4,30,00,000 km
Distance from Paris to England
= 37,00,00,000 + 4,30,00,000 km
= 41,30,00,000 km
= 413 x 10⁶km
In standard form = 4.13 x 10⁸km
Question 20
1 / -0

A teacher asked two of his students to solve the expression and write the answers on the board. Rajeev wrote and Sanjeev wrote . Who wrote the correct answer?

A
Rajeev

B
Sanjeev

C
Both are correct

D
Both are incorrect

Solution

According to the question,

=

=
=

So, Rajeev's answer is correct.

Question 21

1 / -0

Directions: Match the following.

Column - 1	Column - 2
a)	i) -4⁴
b)	ii) 1
c)	iii) 7⁹
d)	iv) 2

a - ii, b - i, c - iv, d - iii

a - iii, b - ii, c - i, d - iv

a - i, b - ii, c - iv, d - iii

a - ii, b - iv, c - i, d - iii

Solution

a] = 1

b] = -4^{9 - 5} = -4⁴

c] = [1 + 1 + 1 + 1] ÷ [1 + 1] = 2

d] = 7^{[15 + 4] - 10} = 7⁹

Question 22
1 / -0

Which of the following options is correct with respect to the two statements given below?

(i) 9⁰ = (10000)⁰(ii) 100 × 100¹¹ = 10000¹¹

A
Both (i) and (ii) are true.

B
Only (i) is true.

C
Only (ii) is true.

D
Neither (i) nor (ii) is true.

Solution

(i) 9⁰ = (10000)⁰
L.H.S: 9⁰ = 1 (∵ a⁰ = 1, where a can be any number)
R.H.S: (10000)⁰ = 1
L.H.S. = R.H.S.
∴ (i) is true.

(ii) 100 × 100¹¹ = 10000¹¹
L.H.S: 100 × 100¹¹ = 100¹¹⁺¹
= 100¹²
R.H.S = 10000¹¹= (100 × 100)¹¹= (100²)¹¹=100²²
L.H.S. R.H.S.
∴ (ii) is false.

Hence, (2) is the correct option.

Question 23

1 / -0

Directions: Compare the following and put the correct sign (=, < or >) in place of question mark (?).

1) (-4)^-2? 3^-2
2) (4)³÷ (4)⁶ ? ()²
3) (

)^-3 + (

)^-3? (3^-2 × 4^-2 × 5^-2)^-1

Options	1	2	3
A	<	=	<
B	<	<	=
C	=	>	<
D	>	=	<

A

B

C

D

Solution

1) (-4)^-2? 3^-2LHS, (-4)^-2=

RHS = 3^-2=

Since,

Therefore,
(-4)^-2 < 3^-2

2) (4)³÷ (4)⁶ ? ()²LHS, (4)³÷ (4)⁶= (4)^{3 - 6}= (4)^{-3 ₌}

RHS, (

)²=

Therefore,
(4)³ ÷ (4)⁶ = (

)²
3) ()^-3 + ()^-3 + ()^-3? (3^-2 × 4^-2 × 5^-2)^-1
Now, (

)^-3 + (

)^-3= 3³ + 4³ + 5³= 27 + 64 + 125
= 216
Now, (3^-2 × 4^-2 × 5^-2)^-1= (3² × 4² × 5²)¹= (3² × 4² × 5²)
= (9 × 16 × 25)
= 3600
Since, 216 < 3600
Therefore,
()^-3 + ()^-3 + ()^-3< (3^-2 × 4^-2 × 5^-2)^-1
Hence, option (A) is correct.

Question 24

1 / -0

Directions: State T for true and F for false.

P) A number is said to be in the standard form, if it is expressed as the product of a number between 1 and 10 and the integral power of 10.
Q) (-5)⁵is smaller than .
R) Very small numbers cannot be expressed in standard form using negative exponents.

	P	Q	R
A	F	F	T
B	F	T	T
C	T	T	F
D	T	F	F

A

B

C

D

Solution

1) A number is said to be in the standard form, if it is expressed as the product of a number between 1 and 10 and the integral power of 10.
Hence, true.

2) Here, (-5)⁵= (-5) × (-5) × (-5) × (-5) × (-5)
= -3125
Also, = (-5)⁵= -3125
Therefore, -3125 = -3125
Hence, true.

3) Very small numbers can be expressed in standard form using negative exponents.
Hence, false.

Question 25
1 / -0

Directions: State T for true and F for false.

1. x^a.x^bis equal to x^{a + b}.
2. Standard form of 57,00,00,000 is 5.7 × 10⁸.
3. The base and power in [25 × 4]^-5 is -100 and 5, respectively.
4. 7³ is greater than 5⁴.

A
T T T T

B
T T F F

C
F T F T

D
F F F T

Solution

1. x^a.x^b is equal to x^{a + b}.
If the bases are same when multiplying, then powers are added.

2. Standard form of 57,00,00,000 is 57 × 10⁷It can be written as 5.7 × 10⁸.

3. The base and power in [25 × 4]^-5 is 100 and -5, respectively.

4. 7³ is greater than 5⁴.
7³ = 7 × 7 × 7 = 343 and 5⁴ = 5 × 5 × 5 × 5 = 625
So, 343 < 625

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Re-Attempt Weekly Quiz Competition

Exponents And Powers Test - 6

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Exponents And Powers Test - 6

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SHARING IS CARING

Question 1

115

125

135

145

Solution

Question 2

100

121

144

164

Solution

Question 3

Solution

Question 4

4

10

12

80

Solution

Question 5

0

1

2

3

Solution

Question 6

Solution

Question 7

Solution

Question 8

8

2

-2

-15

Solution

Question 9

Solution

Question 10

0.0000000089

0.000000089

0.0000089

0.00000089

Solution

Question 11

3

4

5

6

Solution

Question 12

Solution

Question 13

Solution

Question 14

3002

3303

3130

2938

Solution

Question 15

Solution

Question 16

49

165

419

None of these

Solution

Question 17

Rs. 18 x 109

Rs. 18 x

Rs. 18 x 1010

4⁹

16⁵

4¹⁹

Rs. 18 x 10⁹

Rs. 18 x 10¹⁰

Rs. 18 x 10⁷

3.5450 x 10¹⁶

3.8885 x 10¹⁶

3.4513 x 10¹⁶

3.8881 x 10³²

4.13 x 10⁶km

4.13 x 10⁸km

5.23 x 10⁸km