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This mock test of Test: Exponents And Powers - 3 for Class 7 helps you for every Class 7 entrance exam.
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QUESTION: 1

2^{3}+2^{3}+2^{3}+2^{3 }is equal to ____.

Solution:

We have

2^{3}+2^{3}+2^{3}+2^{3 }= 4 × (2^{3})

= 2^{2 }× 2^{3 }= 2^{5}

QUESTION: 2

The value of is ____.

Solution:

= 0

QUESTION: 3

{(1/3)^{−3}−(1/2)^{−3}} ÷ (1/4)^{−3 }?

Solution:

{(1/3)^{−3}−(1/2)^{−3}} ÷ (1/4)^{−3} = {(3)^{3}−(2)^{3}} ÷ (4)^{3} = {27−8} ÷ 64 = 19/64

QUESTION: 4

The value of (−8) × (−8) × (−8) × (−8) × (−8) + (−8) × (−8) × (−8) × (−8) × (−8) is ____.

Solution:

(−8)^{5}+ (−8)^{5 }= −2×(8)^{5} = −2×(2)^{15}

= −(2)^{16} = −(4)^{8}

QUESTION: 5

If (5/3)^{−5 }× (5/3)^{11 }= (5/3)^{8+x}, then x = ?

Solution:

(5/3)^{−5} × (5/3)^{11} = (5/3)^{8+x}

⇒ (5/3)^{−5+11 }= (53)^{8+x }

⇒ (5/3)^{6} = (5/3)^{8+}

On comparing, we get,

8 + x = 6

⇒ x = −2

QUESTION: 6

The value of is ________.

Solution:

=(a^{−2+3} × b^{−3+4})

= a×b

= ab

QUESTION: 7

{(3/4)^{−1}−(1/4)^{−1}}^{−1 }= ?

Solution:

{(3/4)^{−1}−(1/4)^{−1}}^{−1 }= {4/3−4}^{−1} = {−8/3}^{−1}=−3/8

QUESTION: 8

Express the given number using exponential notation: 3125

Solution:

3125 = 5 × 5 × 5 × 5 × 5 = 5^{5}

QUESTION: 9

If (5/9)^{4 }× (5/9)^{−10} = (5/9)^{−4}(5/9)^{2a−1},then the value of a is _____.

Solution:

Equating the powers,

-6=2a-5

2a=-1

a=-1/2

QUESTION: 10

Which of the following is equivalent to 7.7×10^{−6 }?

Solution:

7.7×10^{−6} = 7.7/100000 = 0.0000077

QUESTION: 11

If (3/2)^{2} × (3/2)^{a+5} = (3/2)^{8}, then a = ____.

Solution:

(3/2)^{2 }× (3/2)^{a+5} = (3/2)^{8}

⇒(3/2)^{a+7} = (3/2)^{8}

On comparing, we get,

a+7 = 8 ⇒ a =1

QUESTION: 12

The number which is multiplied by (−8)^{−1} to obtain a product equal to 10^{−1} is ____.

Solution:

Let the number be x, Then, (−8)^{−1}× x = (10)^{−1}

⇒(−1/8) × x = (1/10) ⇒ x= −4/5

QUESTION: 13

The value of

Solution:

**Correct Answer :- b**

**Explanation : ** [(2*3)^{12} * (5*7)^{28} * (5*3)^{16}]/[(7*2)^{12} * (7*3)^{11} * 5^{28}]

= [(2)^{12} * (3)^{12} * (5)^{28} * (7)^{28} * (5)^{16} * (3)^{16}]/[(7)^{12} * (2)^{12} * (7)^{11} * (3)^{11} * (5)^{28}]

= [(2)^{12} * (3)^{12+16} * (5)^{28+16} * 3^{16}]/[(7)^{12+11} * (2)^{12} * (3)^{11 }* (5)^{28}]

= [(2)^{12} * (3)^{28} * (5)^{44} * 3^{16}]/[(7)^{23} * (2)^{12} * (3)^{11 }* (5)^{28}]

= 3^{17} * 5^{16} * 7^{5}

QUESTION: 14

The value of a^{b }− b^{a}, if a = 3, b = 7 is

Solution:

a^{b} − b^{a} =3^{7}−7^{3 }= 2187−343 = 1844

QUESTION: 15

The value of (23/25)^{0 }× (−1/2)^{5 }×2^{3 }× (3/4)^{2 }is

Solution:

(23/25)^{0 }× (−1/2)^{5 }×2^{3 }× (3/4)^{2}

=1×(−1)^{5 }× (2)^{−5 }× 2^{3 }× 3^{2 }× (2)^{−4}=−9/64

QUESTION: 16

A rectangular piece of land is to be sold off in smaller pieces. The total area of the land is 217 sq. miles. The pieces to the cut out are 162 sq. miles in size. How many smaller pieces of the land can be sold at the given size?

Solution:

Required number of pieces

QUESTION: 17

Pooja spends about Rs.40000 each month on utensils hold. If she has about 1×10^{8 }utensils, what is the total amount of money (in Rs.) spent on the households in one month?

Solution:

Total amount of money spent Rs.(40000×1×10^{8}) = Rs.(4.0×10^{12})

QUESTION: 18

All the planets revolve around the Sun in elliptical orbits. Uranus's farthest distance from the Sun is approximately 3.004×10^{9} km and its closest distance is approximately 2.7499×10^{9} kmkm. What is the average distance of Uranus from the Sun?

Solution:

Distance of Uranus from Sun =(3.004×10^{9})km

Uranus closest distance from Sun =(2.7499×10^{9})km

Total distance = 3.004×10^{9 }+ 2.7499×10^{9}

= (5.753×10^{9})km

Average distance = (5.753×10^{9})/2

= (2.8765×10^{9})km

QUESTION: 19

There are three places A, B, C in a straight line as shown below. If distance between place A and B is (2.4×10^{6})m and distance between 8 and C is (5.2×10^{5})m, then find the distance between place A and C in standard form.

Solution:

Distance between place A and B

= 2.4×10^{6}m = 2400000 m

Distance between place 6 and C = 5.2×10^{5} m = 5.2×100000 m = 520000 m

Distance between place A and C

= (2.4×10^{6 }+ 5.2×10^{5})m = (2400000 + 520000)m = 292×10^{4}m

Standard form of 292×10^{4}m = 2.92×10^{6}

QUESTION: 20

Mr Gupta asked two of his students to solve the expression and write the answer on blackboard. Aryan wrote the answer as 3a^{−4}b^{5 }whereas Ayan wrote the answer as . Who wrote the correct answer?

Solution:

We have,

= 3a^{−4}b^{5}

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