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AP Board Class 7 Maths Chapter 8 Exponents and Powers Ex 8.2 Textbook Solutions PDF: Download Andhra Pradesh Board STD 7th Maths Chapter 8 Exponents and Powers Ex 8.2 Book Answers

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Andhra Pradesh State Board Class 7th Maths Chapter 8 Exponents and Powers Ex 8.2 Books Solutions

Board	AP Board
Materials	Textbook Solutions/Guide
Format	DOC/PDF
Class	7th
Subject	Maths
Chapters	Maths Chapter 8 Exponents and Powers Ex 8.2
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AP Board Class 7th Maths Chapter 8 Exponents and Powers Ex 8.2 Textbooks Solutions with Answer PDF Download

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Question 1.
Simplify the following by using Laws of Exponents.
(i) 3⁷ × 3⁸
Answer:
3⁷ × 3⁸
We know a^m × aⁿ = a^m+n
3⁷ × 3⁸ = 3⁷ + 8 = 3¹⁵
∴ 3⁷ × 3⁸ =3¹⁵

(ii) 9² × 9⁰ × 9³
Answer:
9² × 9⁰ × 9³
We know a^p × a^q × a^r = p + q + r
9² × 9⁰ × 9³ = 9^{2 + 0 + 3} = 9⁵
∴ 9² × 9⁰ × 9³ = 9⁵

(iii) (2⁸)³
Answer:
(2⁸)³
We know (a^m)ⁿ = a^mn
(2⁸)³ = 2^8×3 =2²⁴
∴ (2⁸)³ = 2²⁴

(iv) (a⁵)⁴
Answer:
(a⁵)⁴
We Know (a^m)ⁿ = a^mn
(a⁵)⁴ = a^5×4 = a²⁰
(a⁵)⁴ = a²⁰

(v) (25)4×(25)3×(25)8
Answer:

(vi) 7⁵ ÷ 7⁸
Answer:
7⁵ ÷ 7⁸
We know a^m = 1𝑎𝑛−𝑚 (n>m)
7⁵ ÷ 7⁸ = 178−5=173
∴ 7⁵ ÷ 7⁸ = 173

(vii) (−6)9(−6)5
Answer:
(−6)9(−6)5
We Know a^m ÷ aⁿ = a^m-n(m > n)
(−6)9(−6)5 = (-6)^9-5 = (-6)⁴
∴ (−6)9(−6)5 = (-6)⁴

(viii) (6⁴ × 6²) ÷ 6⁵
Answer:
(6⁴ × 6²) ÷ 6⁵
We know atm X a = a”
= (6⁴⁺²) ÷ 6⁵
= 6⁶ ÷ 6⁵
We know a^m ÷ aⁿ = a^m-n (m> n)
= 6^6-5 = 6¹ = 6
∴ (6⁴ × 6²) ÷ 6⁵ = 6

(ix) 5323
Answer:
5323
We know 𝑎𝑚𝑏𝑚=(𝑎𝑏)𝑚
∴ 5323=(52)3

(x) (-3)³ × (-3)¹⁰ × (-3)⁷
Answer:
(-3)³ × (-3)¹⁰ × (-3)⁷
we know a^p . a^q. a^r = a^p+q+r
(-3)³ × (-3)⁰ × (-3)⁷ = (-3)³⁺¹⁰⁺⁷
∴ (- 3)³ × (- 3)¹⁰ × (- 3)⁷ = (- 3)²⁰

Question 2.
Simplify and express each of the following in Exponential form.
(i) (𝑎5𝑎3) × a⁸
Answer:
(𝑎5𝑎3) × a⁸
We Know 𝑎𝑚𝑎𝑛 = a^m-n(m > n)
= (a^5-3) × a⁸
= a² × a⁸

We know a^m × aⁿ = a^m+n
= a²⁺⁸ = a¹⁰
∴ (𝑎5𝑎3) × a⁸ = a¹⁰

(ii) 2⁰ + 3⁰ – 4⁰
Answer:
2⁰ + 3⁰ – 4⁰
We know a⁰ = 1

∴ 2⁰ + 3⁰ – 4⁰ = 1

(iii) (2³ × 2)²
Answer:
(2³ × 2)²
We know a^m.aⁿ = a^m+n
(2³ × 2)² = (2³⁺¹)² = (2⁴)²

We know (a^m)ⁿ = a^m.n
= 2^4×2 = 2⁸
∴(2³ × 2)² = 2⁸

(iv) [(5²)³ × 5⁴] ÷ 5⁷
Answer:
[(5²)³ × 5⁴] ÷ 5⁷

We know (a^m) = a^m.n
= [5^2×3 × 5⁴] ÷ 5⁷
= [5⁶ < 5⁴] ÷ 5⁷

We know a^m .aⁿ = a^m+n
= [5⁶⁺⁴] ÷ 5⁷
= 5¹⁰ ÷ 5⁷
We know a^m ÷ aⁿ = a^m-n (m > n)
= 5^10-7 = 5³
∴ [(5²)³ × 5⁴] ÷ 5⁷ = 5³

Question 3.
Simplify (𝑥𝑎𝑥𝑏)×(𝑥𝑏𝑥𝑐)×(𝑥𝑐𝑥𝑎)
Answer:
(𝑥𝑎𝑥𝑏)×(𝑥𝑏𝑥𝑐)×(𝑥𝑐𝑥𝑎)

Question 4.
Find the value of the following.
(i) (-1)¹⁰⁰⁰
Answer:
(-1)¹⁰⁰⁰
(-1)¹ = – 1
(-1)² = – 1 × – 1 = + 1
(-1)³ = – 1 × -1 × -1 = – 1
(-1)⁴ = -1 × -1 × – 1 × – 1 = + 1
(-1)⁵ = -1 × -1 × -1 × -1 × -1 = -1
(-1)¹⁰⁰ = -1 × -1 × -1 × ………… 100 times = + 1

So, (-1)^{odd number} = -1 and
(-1)^{even number} = + 1

Here 1000 is even number
So, (-1)¹⁰⁰⁰ = + 1

(ii) (1)²⁵⁰
Answer:
1²⁵⁰ = 1 × 1 × 1 ……… 250 times = 1
∴ 1²⁵⁰ = 1

(iii) (1)¹²¹
Answer:
1¹²¹ = -1 × -1 × -1 ……..(121 times)
Here 121 is an odd number
So, (1)¹²¹ = – 1

(iv) (10000)⁰
Answer:
(10000)⁰
we know a⁰ = 1
So, (10000)⁰ = 1

Question 5.
If 7⁵ × 7^3x = 7²⁰ then find the value of ’x’.
Answer:
Given, 7⁵ × 7^3x = 7²⁰
W know a^m X aⁿ = a^m+n
7^{5 + 3x} = 7²⁰
If the bases are equal, then the powers should also be equal.
⇒ 5 + 3x = 20
⇒ 5 + 3x – 5 = 20 – 5
⇒ 3x = 15
⇒ 3𝑥3=153 = 5
∴ x = 5

Question 6.
If 10^y = 10000 then 5y =?
Answer:
Given, 10^y = 10000
10^y = 10 × 10 × 10 × 10
10^y = 10⁴
If the bases are equal, then the powers should also be equal.
⇒ y = 4
Multiply by 5 on bothsides,
5 × y = 5 × 4
∴ 5y = 20

Question 7.
If 5^x = 100 then find the following values.
(i) 5^x+y
Answer:
Given 5^x+y = 100
5^x = 10²
Multiply by 5²
5^x × 5² = 100 × 5²
5^x+2 = 100 × 25 (∵ a^m × aⁿ = a^m+n)
∴ 5^x+2 = 2500

(ii) 5^x-2
Answer:
Given 5^x = 100
5^x = 10²
Divide by 5² on both sides
5^x ÷ 5² = 100 ÷ 5²

∴ 5^x-2 = 4

Question 8.
By what number should 3⁴ be multiplied so that the product is 243?
Answer:
Given number is 3⁴
If we multiply 3⁴ by ‘a’ the product is 243.
i.e. 3⁴ × a = 243
= 3 × 3 × 3 × 3 × 3
3⁴ × a = 35
Divide by 3⁴ on both sides

If we multiply 3⁴ by 3 we get 243.

Question 9.
Arushi computed (5²)⁴ as 5¹⁶ Has she done it correctly or not’? Justify your answer.
Answer:
Given, (5²)⁴
We know) (a^m)ⁿ = a^m.n
= 5^2×4 = 5⁸
∴ (5²)⁴ = 5⁸
But Arushi got 5¹⁶ So, (5²)⁴ ≠ 5¹⁶
Therefore Arushi did wrong.

Question 10.
Is 3⁵ × 4⁵ equal to 12²⁵? If not why? Justify your answer.
Answer:
Given, 3⁵ × 4⁵
We know a^m × b^m = (a × b)^m
So, 3⁵ × 4⁵ = 12 but not 12^5×5
= (3 × 4)⁵
= (12)⁵
3⁵ × 4⁵= 12⁵
But given 3⁵ × 4⁵ = 12²⁵.
So, this is wrong.
So, 3⁵ × 4⁵ ≠ 12²⁵

AP Board Textbook Solutions PDF for Class 7th Maths

Andhra Pradesh Board Class 7th Maths Chapter 8 Exponents and Powers Ex 8.2 Textbooks for Exam Preparations

Andhra Pradesh Board Class 7th Maths Chapter 8 Exponents and Powers Ex 8.2 Textbook Solutions can be of great help in your Andhra Pradesh Board Class 7th Maths Chapter 8 Exponents and Powers Ex 8.2 exam preparation. The AP Board STD 7th Maths Chapter 8 Exponents and Powers Ex 8.2 Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 7th Maths Chapter 8 Exponents and Powers Ex 8.2 Books State Board syllabus with maximum efficiency.

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