RBSE Class 7 Maths Important Questions Chapter 13 Exponents and Powers

Rajasthan Board RBSE Class 7 Maths Important Questions Chapter 13 Exponents and Powers Important Questions and Answers.

RBSE Class 7 Maths Chapter 13 Important Questions Exponents and Powers

Multiple Choice Questions

Question 1.
The value of \(\left(\frac{-5}{6}\right)^{0}\) is:
(a) 0
(b) 1
(c) - \(\frac{5}{6}\)
(d) None of these
Answer:
(b) 1

Question 2.
The value of (- 1)¹⁵ is :
(a) -15
(b) 1
(c) - 1
(d) None of these
Answer:
(c) - 1

Question 3.
In (- 5)⁴ base and power respectively are:
(a) 5 and 4
(b) 4 and - 5
(c) - 5 and 4
(d) - 5 and - 4
Answer:
(c) - 5 and 4

Question 4.
5^x. 5² is equal to :
(a) 5^2x
(b) 5^{x - 2}
(c) 5^{x + 2}
(d) 2^{5 + x}
Answer:
(c) 5^{x + 2}

Question 5.
Exponential notation of (- 343) is :
(a) 3⁷
(b) 7³
(c) (- 7)³
(d) 7^{- 3}
Answer:
(c) (- 7)³

Question 6.
(5⁰ + 3⁰ + 2⁰) is equal to :
(a) 10⁰
(b) 1
(c) 3
(d) 30⁰
Answer:
(c) 3

Question 7.
Standard form of 370.25 is :
(a) 3 × 10⁴
(b) 3.7025 × 10²
(c) 3.7025 × 10^{- 4}
(d) 3 × 10^{- 4}
Answer:
(b) 3.7025 × 10²

Question 8.
Usual form of 3.07 × 10⁴ is :
(a) 307
(b) 3.07
(c) 30700
(d) None of these
Answer:
(c) 30700

Fill in the Blanks

Question 1.
6³ is read as 6 ........................ to power of 3.
Answer:
raised

Question 2.
If a and b are non-zero integers and m is a whole numbers, then a^m × b^m = ..........................
Answer:
(ab)^m

Question 3.
\(\frac{32}{243}\) is expressed m power notation as ...............................
Answer:
\(\left(\frac{2}{3}\right)^{5}\)

Question 4.
376 in standard form can be written as 3.76 × ...............................
Answer:
10²

Question 5.
Usual form of 3.8 × 10⁵ is ..................................
Answer:
5.380000

State whether True or False

Question 1.
In 25 base is 5 and exponent is 2.
Answer:
False

Question 2.
57 is read as 5 raised to the power 7.
Answer:
True

Question 3.
We use exponents to make large numbers easy to read, understand and compare.
Answer:
True

Question 4.
If a is a non-zero integers and 'm' and 'n' are whole numbers, then (a^m)ⁿ = a^{m + n}.
Answer:
False

Question 5.
Standard form of 20,00,000 is 2 × 106.
Answer:
True

Very Short Answer Type Questions

Question 1.
Express each of the following numbers as a product of powers of their prime factors:
(i) 36
Answer:
36 = 2 × 2 × 3 × 3 = 2² × 3²

(ii) 675
Answer:
675 = 3 × 3 × 3 × 5 × 5 = 3³ × 5²

Question 2.
Express each of the following numbers as a product of powers of their prime factors:
(i) 450
Answer:
450 = 2 × 3 × 3 × 5 × 5 = 2 × 3² × 5²

(ii) 2800
Answer:
2800 = 2 × 2 × 2 × 2 × 5 × 5 × 7 = 2⁴ × 5² × 7

Question 3.
Express each of the following as a rational number of the form \(\frac{p}{q}\):
(i) \(\left(\frac{3}{7}\right)^{2}\)
Answer:
\(\left(\frac{3}{7}\right)^{2}=\frac{3 \times 3}{7 \times 7}=\frac{9}{49}\)

(ii) \(\left(\frac{7}{9}\right)^{3}\)
Answer:
\(\left(\frac{7}{9}\right)^{3}=\frac{7 \times 7 \times 7}{9 \times 9 \times 9}=\frac{343}{729}\)

Short Answer Type Questions

Question 1.
Write the following numbers in the usual form:
(i) 4.83 × 10⁷
Answer:
4.83 × 10⁷ = 483 × 10^{(7 - 2)}
= 483 × 10⁵ = 4,83,00,000
Since, the decimal point is moved one place to the right.

(ii) 3.21 × 10⁵
Answer:
3.21 × 10⁵ = 321 × 10^{(5 - 2)}
= 321 × 10³
= 3,21,000
Since, the decimal point is moved two places to the right.

(iii) 315 × 10³
Answer:
3.5 × 10³ = 35 × 10^{(3 - 1)}
= 35 × 10² = 3,500
Since, the decimal point is moved one place to the right.