RBSE Solutions for Class 8 Maths Chapter 3 Powers and Exponents Additional Questions

RBSE Solutions for Class 8 Maths Chapter 3 Powers and Exponents Additional Questions is part of RBSE Solutions for Class 8 Maths. Here we have given Rajasthan Board RBSE Class 8 Maths Chapter 3 Powers and Exponents Additional Questions.

Board	RBSE
Textbook	SIERT, Rajasthan
Class	Class 8
Subject	Maths
Chapter	Chapter 3
Chapter Name	Powers and Exponents
Exercise	Additional Questions
Number of Questions	41
Category	RBSE Solutions

Rajasthan Board RBSE Class 8 Maths Chapter 3 Powers and Exponents Additional Questions

I. Objective Type Questions

Question 1.
Meaning of 2⁵ ÷ 2² is
(a) 2⁵⁺²
(b) 2^5-2
(c) 2^5/2
(d) (2⁵)²

Question 2.
The value of 3⁰ is
(a) 0
(b) 2
(c) 1
(d) 4

Question 3.
The power in \({ \left( -\frac { 8 }{ 3 } \right) }^{ 24 }\) is
(a) 3
(b) 8
(c) 24
(d) 12

Question 4.
The value of \(\left( \frac { 1 }{ { 2 }^{ -2 } } \right) \) will be
(a) 2
(b) 4
(c) \(\frac { 1 }{ 2 }\)
(d) 1

Question 5.
Simplest form of (2 x 4)² is
(a) 2² x 4²
(b) \(\frac { { 2 }^{ 2 } }{ { 4 }^{ 2 } } \)
(c) 2² + 4²
(d) \(\frac { { 4 }^{ 2 } }{ { 2 }^{ 2 } } \)

Question 6.
Form of Exponent in (4)⁹ x (4)³ is
(a) (4)³
(b) (27)
(c) (4)¹²
(d) (4)⁶

Question 7.
The value of (3⁵ x 3³) ÷ (3)¹⁴ is

Question 8.
The value of (-1)¹⁰¹ equal to
(a) 1
(b) – 1
(c) 0
(d) 101

Question 9.
2000000 is expressed in standard form as
(a) 0.2 x 10⁵
(b) 2.0 x 10⁶
(c) 10.2 x 10⁶
(d) 10.2 x 10⁵

Question 10.
\({ \left( \frac { 3 }{ 4 } \right) }^{ x }\div { \left( \frac { 3 }{ 4 } \right) }^{ 2 }={ \left( \frac { 3 }{ 4 } \right) }^{ 5 }\) then what value of x equal to
(a) 7
(b) 3
(c) \(\frac { 5 }{ 2 }\)
(d) -3

Answers.
1. (b)
2. (c)
3. (c)
4. (b)
5. (a)
6. (c)
7. (b)
8. (b)
9. (b)
10. (a)

II. Fill in the blanks

Question 1.
Exponential form of \(\frac { 3 }{ 4 } \times \frac { 3 }{ 4 } \times \frac { 3 }{ 4 } \) is ………..

Question 2.
If a is a non zero rational number and n is a positive integer then a^-n = ……..

Question 3.
A number is(RBSESolutions.com)called in …….. form if it is expressed in K x 10ⁿ, n = an integer

Question 4.
In \({ \left( \frac { 4 }{ 5 } \right) }^{ 50 }\), then power is …… and base is …..

Question 5.
Positive exponential form of 5^-2 is …….

Answers
1. \({ \left( \frac { 3 }{ 4 } \right) }^{ 3 }\)
2. \(\frac { 1 }{ { a }^{ n } } \)
3. standard,
4. 50, \(\frac { 4 }{ 5 }\)
5. \(\left( \frac { 1 }{ { 5 }^{ 2 } } \right) \)

III. True/False Type Questions

Questions 1.
The standard form of 100000000000 is 1.0 x 10¹¹

Question 2.
The value of (- 2a)³ is equal to 8a³

Question 3.
The value of (2⁰ + 3⁰) x 4⁰ is equal to 2

Question 4.
Value of \({ \left( \frac { 9 }{ 8 } \right) }^{ -3 }\times { \left( \frac { 8 }{ 9 } \right) }^{ -3 }\) is equal to \(\frac { 8 }{ 9 }\)

Answers
1. True
2. True
3. False
4. True

IV Very Short Answer Type Questions

Question 1.
Write the exponential form of \(\frac { 5 }{ 6 } \times \frac { 5 }{ 6 } \times \frac { 5 }{ 6 } \times \frac { 5 }{ 6 } \)
Solution
\({ \left( \frac { 5 }{ 6 } \right) }^{ 4 }\)

Question 2.
Write the exponential form of 729.
Solution
729 = 3 × 3 × 3 × 3 × 3 × 3
= (3)⁶ Ans.

Question 3.
Write the(RBSESolutions.com)exponential form of

Solution
\({ \left( \frac { 2 }{ 5 } \right) }^{ 3 }\times { \left( \frac { 3 }{ 5 } \right) }^{ 2 }\)

Question 4.
Find the value \({ \left( \frac { 1 }{ 3 } \right) }^{ 3 }\times { \left( \frac { 2 }{ 3 } \right) }^{ 4 }\)
Solution
\({ \left( \frac { 1 }{ 3 } \right) }^{ 3 }\times { \left( \frac { 2 }{ 3 } \right) }^{ 4 }\)

Question 5.
Write the exponential form of \({ \left[ \left( { 4 }^{ 3 }\times { 4 }^{ 4 } \right) \div { 4 }^{ 9 } \right] }^{ 2 }\)
Solution
\({ \left[ \left( { 4 }^{ 3 }\times { 4 }^{ 4 } \right) \div { 4 }^{ 9 } \right] }^{ 2 }\)

Question 6.
If \({ 2 }^{ \frac { a }{ b } }=1\) then find the value of a.
Solution
\({ 2 }^{ \frac { a }{ b } }={ 2 }^{ 0 }\)
\({ 2 }^{ \frac { a }{ b } }=1\)
\(\frac { a }{ b }\) = 0
∴ a = 0
Base are same so power will be equal.

Question 7.
If a = 2,b = 3 then find the(RBSESolutions.com)value of (a^b + b^a)^-1.
Solution
(a^b + b^a)^-1
= (2³ + 3²)^-1
= (2 × 2 × 2 × 3 × 3)^-1
= (8 + 9)^-1
= (17)^-1
= \(\frac { 1 }{ 17 }\)

Question 8.
Evaluate
(i) 3² × 3³
(ii) \({ \left[ { \left( \frac { -1 }{ 2 } \right) }^{ 3 } \right] }^{ 2 }\)
Solution
(i) 3² x 3³ = 3²⁺³ = 3⁵ = 243

V. Short Answer Type Questions.

Question 1.
Find the value of \({ \left[ { \left( 343 \right) }^{ -2 } \right] }^{ \frac { 1 }{ 3 } }\).
Solution
\({ \left[ { \left( 343 \right) }^{ -2 } \right] }^{ \frac { 1 }{ 3 } }\)

Question 2.
Prove that
(x^a-b)^a+b (x^b-c)^b+c (x^c-a)^c+a = 1
Solution
(x^a-b)^a+b (x^b-c)^b+c (x^c-a)^c+a
= x^(a-b)(a+b) x^(b-c)(b+c) x^(c-a)(c+a)
= x^a²-b² x^b²-c² x^c²-a²
∵ (a + b)(a – b) = a² – b²
= x^{a²-b²+b²-c²+c²-a²}
= x⁰
= 1

Question 3.
Write in assending order(RBSESolutions.com)magnitude of following
\({ \left( 3 \right) }^{ \frac { 1 }{ 4 } },{ \left( 2 \right) }^{ \frac { 1 }{ 3 } },{ \left( 4 \right) }^{ \frac { 1 }{ 3 } }\)
Solution.
LCM of 4,3 and 3 is 12

Question 4.
Prove that

Solution

Question 5.
Solve

Solution

Question 6.
Find the value of p if
5^p-3 x 3^2p-8 = 225
Solution
5^p-3 x 3^2p-8 = 225
or, 5^p-3 x 3^2p-8 = 5 x 5 x 3 x 3 = 5² x 3²
or, p – 3 = 2
or, 2p – 8 = 2
or, p = 5

Question 7.
If (- 2)^x+1 x (- 2)³ = (- 2)⁵ then find the value of x.
Solution
(- 2)^x+1 x (- 2)³ = (- 2)⁵
or (- 2)^x+1+3 = (- 2)⁵
or (- 2)^x+4 = (- 2)⁵
∵ Base are(RBSESolutions.com)same, so power can be equal
x + 4 = 5
or x = 5 – 4 = 1

Question 8.
Find the value of

Solution.

Question 9.
Write standard form of(RBSESolutions.com)the following numbers
(a) 10350000
(b) 0.0007305
Solution
(a) 10350000 = 1,035 × 10000000
= 1.035 × 10⁷

Question 10.
The size of a red blood cell is 0.000007 m and the size of a plant cell is 0.00001275 m. Compare.
Solution
Size of red blood cell = 0.000007
= 7 × 10^-6 m
Size of plant cell = 0.00001275 m
= 1.275 × 10^-5 m

Hence, a red blood cell is half a plant cell.

Question 11.
Express in standard form
(i) 15,00,00,000
(ii) 0.0000067
Solution
(i) 15,00,00,000
= 15 × 1,00,00,000
= 15 × 10⁷

Question 12.
If, (243)^x+1 = (243)^-5 then find the value of x.
Solution
243^x+1 = (243)^-5
Since the bases(RBSESolutions.com)are same.
∴Powers are put equivalent
x + 1 = -5
x = – 5 – 1
x = – 6

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