Exponents And Powers(7th Grade > Mathematics ) Questions and answers for exam Preparation

7th Grade > Mathematics

EXPONENTS AND POWERS MCQs

Total Questions : 102 | Page 1 of 11 pages

Question 1. Simplify : [3 MARKS]

\frac{3^{8} \times 4^{5} \times 3^{2} \times 5^{4} \times 7^{5}}{3^{9} \times 4^{4} \times 7^{5}}

Discuss Question

:
Concept: 1 Mark
Steps: 1 Mark
Answer: 1 Mark
Given,

\frac{3^{8} \times 4^{5} \times 3^{2} \times 5^{4} \times 7^{5}}{3^{9} \times 4^{4} \times 7^{5}}

= \frac{3^{8 + 2} \times 4^{5} \times 5^{4} \times 7^{5}}{3^{9} \times 4^{4} \times 7^{5}}

[

∵ a^{m} \times a^{n} = a^{m + n}

]

= 3^{10 - 9} \times 4^{5 - 4} \times 5^{4} \times 7^{5 - 5}

[

∵ \frac{a^{m}}{a^{n}} = a^{m - n}

]

= 3^{1} \times 4^{1} \times 5^{4} \times 7^{0}

= 3 \times 4 \times 5^{4}

[

∵ a^{0} = 1

]

= 7500

Question 2. Express

512 \times 729

in exponential form:

28×33
29×36
27×34
29×37

Discuss Question

Answer: Option B. -> 29×36
:
B

512 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^{9}

729 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 3^{6}

2^{9} \times 3^{6}

Question 3.

7^{2} \times 2^{2}

=___

Discuss Question

7^{2} = 49

2^{2} = 4

7^{2} \times 2^{2} = (7 \times 2)^{2} = 14^{2} = 196

Question 4. In

10^{4}

,10 is called the __ and 4 is called the exponent.

Discuss Question

:
Here, 10 is called the base.

Question 5. If abc = 1, then find the value of:

\frac{1}{1 + a + b^{- 1}} + \frac{1}{1 + b + c^{- 1}} + \frac{1}{1 + c + a^{- 1}}

[4 MARKS]

Discuss Question

:
Formula: 1 Mark
Steps: 2 Marks
Answer: 1 Mark
Given that,
abc=1
So,

c = 1 \div a b = (a b)^{- 1}

Similarly,

a = (b c)^{- 1}

b = (a c)^{- 1}

And,

a b = c^{- 1}

a c = b^{- 1}

b c = a^{- 1}

\frac{1}{1 + a + b^{- 1}} + \frac{1}{1 + b + c^{- 1}} + \frac{1}{1 + c + a^{- 1}}

= \frac{1}{1 + a + b^{- 1}} + \frac{b^{- 1}}{b^{- 1} + b b^{- 1} + b^{- 1} c^{- 1}} + \frac{a}{a + a c + a a^{- 1}}

[Multiplying 2nd term by

\frac{b^{- 1}}{b^{- 1}}

and 3rd term by

\frac{a}{a}

]

= \frac{1}{1 + a + b^{- 1}} + \frac{b^{- 1}}{b^{- 1} + 1 + a} + \frac{a}{a + b^{- 1} + 1}

∵ \frac{a^{m}}{a^{n}} = a^{m - n}

= \frac{1 + b^{- 1} + a}{1 + a + b^{- 1}}

= 1

Question 6. Express 625 as a power of 5. [1 MARK]

Discuss Question

625 = (5) \times (5) \times (5) \times (5)

\Rightarrow 625 = 5^{4}

Question 7. A shopkeeper A has Rs 34265 in his counter and shopkeeper B has 432500 paise in his counter. Express the difference in rupees in standard form. [ 3 MARKS]

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:
Conversion: 1 Mark
Difference: 1 Mark
Standard form: 1 Mark
As per the question
The amount shopkeeper A has = Rs 34265.
The amount shop keeper B has = 432500 paise

\Rightarrow

Rs 4325.
Difference = Rs 34265 - Rs 4325 = Rs 29940.
The standard form of Rs29940.

29940 = 2.994 \times 10^{4}

The difference in rupees is

2.994 \times 10^{4}

Question 8. The distance between two cities is 3245678 km. Convert it into meters and express in standard form. [2 MARKS]

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:
Conversion: 1 Mark
Standard form: 1 Mark
Givendistance that the distance between two cities3245678 km.
Now, 1 km = 1000 m
3245678 km = (3245678

\times

1000)m =3245678000 m.
Standard form is,

3245678000 m = 3.245678 \times 10^{9}

Question 9. Find the value of m and n, if

6^{- 5} \times 5^{- 2} \times 6^{3} \times 5^{m} \times 6^{n} = 1

. [4 MARKS]

Discuss Question

:
Steps: 2 Marks
Application: 1 Mark
Answer: 1 Mark

6^{- 5} \times 5^{- 2} \times 6^{3} \times 5^{m} \times 6^{n} = 1

6^{- 5} \times 6^{3} \times 6^{n} \times 5^{- 2} \times 5^{m} = 1

6^{- 5 + 3 + n} \times 5^{- 2 + m} = 1

6^{- 2 + n} \times 5^{- 2 + m} = 1

The bases of both the numbers are not equal.
So, the value will be equal to 1, when the exponents of these bases will be equal to zero.
Any non - zero number raised to the powerzero is 1.
So, the exponents of both 6 and 5 are zero.
Therefore,

- 2 + m = 0 \Rightarrow m = 2

- 2 + n = 0 \Rightarrow n = 2

∴ m = n

Question 10. The area of a certain number of triangles is equal to the sum of the exponents of the prime factors of the number 1628, and each prime factor represents a triangle. Find the sum of areas of the triangles and find the number of the triangles. [4 MARKS]

Discuss Question

:
Prime factorization: 1 Marks
Number of Triangles: 1 Mark
Sum of the area: 1 Mark
Steps: 1 Mark
Given that,
The area of a certain number of triangles is equal to the exponents of the prime factors of the number 1628 and each prime factor represents a triangle.
Prime factors of 1628 are:

1628 = 2^{2} \times 3 \times 7 \times 19

.
Since there are 5 prime factors,

\Rightarrow

The number of given triangles are = 5
The area of the triangles is the sum of powers of the prime factors.

\Rightarrow

The sum of areas of the triangle = 2 + 1 + 1 + 1
= 5 square units
The number of triangles is 5 and the sum of areas of the triangle is 5 square units.