10 question with heddings from chapter EXPONENTS and POWERS only for 8th class
Answers
Answer:
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Step-by-step explanation:
Answer:
1. Find the value of (40 + 4-1) × 22
Solution:
(40 + 4 -1) × 22 = (1 + ¼) × 4
= 5/4 x 4
= 5
2. Solve 3-4 and (½)-2
Solution:
We know, b-n = 1/bn
So, 3-4 = 1/34 = 1/81
And, (½)-2 = 1-2/2-2 = 22/12 = 4
3. Simplify the following expression and express the result in positive power notation:
(−4)5 ÷ (−4)8
Solution:
Using am ÷ an = am-n
(−4)5 ÷ (−4)8 = (-4)5/(-4)8
⇒ (-4)5-8 = 1/ (-4)3
4. Evaluate a2 × a3 × a-5
Solution:
a2 × a3 × a-5 = a2+3-5
= a5-5
= a0 = 1
5. Express 4-3 as a power with base 2.
Solution:
4-3 can be written as:
4-3 = (22)-3
Now, by using exponential law i.e. (am)n = amn
4-3 = 2-6 (which is in base 2 form).
Long Answer Type Questions
6. Evaluate (√4)-3
Solution:
(√4)-3 = (4½)-3
= 4-3/2 = 1/ 43/2
= 1/(43)½ = 1/(64)½
= 1/(82)½ = 1/8
7. Find the value of x for which 2x ÷ 2-4 = 45
Solution:
Given,
2x ÷ 2-4 = 45
Now, 2x × (½)-4 = (22)5
Or, 2x × (½)-4 = 210
Thus, 2x+4 = 210
⇒ x + 4 = 10
Hence, x + 4 = 10
So, x = 6
8. Calculate the missing value of “x” in the following expression: (11/9)3 × (9/11)6 = (11/9)2x-1
Solution:
Given: (11/9)3 × (9/11)6 = (11/9)2x-1
The multiplier of L.H.S of the equation can be written as:
(11/9)3 × (11/9)-6 = (11/9)2x-1
⇒ (11/9)3-6 = (11/9)2x-1
Therefore, -3 = 2x – 1
2x = -3 + 1
x = -2/2
x = -1
9. 5 books and 5 paper sheets are placed in a stack. Find the total thickness of the stack if each book has a thickness of 20 mm and each sheet has a thickness of 0.016 mm.
Solution:
Given,
Thickness of 1 book = 20 mm
And,
Thickness of one paper = 0.016 mm
So, thickness of 5 books = 20 x 5 = 100 mm
And,
Thickness of 5 papers = 0.016 × 5 = 0.08 mm
Now, the total thickness of a stack is:
= 100 + 0.08 = 100.08 mm
= 100.08 102 / 102 mm
= 1.0008 × 102 mm
10. If a new-born bear weighs 4 kg, calculate how many kilograms a five-year-old bear weigh if its weight increases by the power of 2 in 5 years?
Solution:
Given,
Weight of new-born bear = 4 kg
Rate of weight increase in 5 years = power to 2
Thus, the weight of the 5-year old bear = 42 = 16 kg
Q.11: Simplify [25 x t-4]/[5-3 x 10 x t-8]
Solution:
We can write the given expression as;
[52x t-4]/[5-3 x 5 x 2 x t-8]
= [52 x t-4+8]/[5-3+1 x2]
= [52+2 x t4]/[2]
= [54 x t4]/[2]
= [625/2] t4
Q.12: Express 0.00000000837 in standard form.
Solution:
0.00000000837
= 0.00000000837 x 109 / 109
= 8.37 ×10-9
Q.13: Write 3.61492 x 106 in usual form.
Solution: 3.61492 x 106
= 3.61492 x 1000000
= 3614920