In this page we have Important questions for exponents Class 8 maths Chapter 12 CBSE
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Question 1
Evaluate
- 2^{ -2}
- (- 2)^{ - 2}
- (3/2)^{-5 }
Answer
As we know that
b
^{-n}= 1/b
^{n}
(i) 2
^{-2} = 1/ 2
^{2} =1/4
(ii) (-2)
^{-2} = 1/(-2)
^{2}= 1/4
(iii) (3/2)
^{-5 } =3-
^{5}/ 2
^{-5}
=2
^{5}/3
^{5 }= 32/243
Question 2
Simplify and express the result in power notation with positive exponent.
(i) (-2)
^{5} ÷ (-2)
^{4}
(ii) (1/2)
^{2} × (2/5)
^{2}
(iii) (-5)
^{2} × (3/5)
Answer
(i) (-2)
^{5} ÷ (-2)
^{4}
= (-2)
^{5} / (-2)
^{4}
= (-2)
^{5-4}
=-2
(ii) (1/2)
^{2} × (2/5)
^{2}
= (1/4) X (4/25)
= 1/25
iii) (-5)
^{2} × (3/5)
=25 × (3/5)
=15
Question 3
Find the value of.
- (4^{0} + 4^{ - 1}) × 2^{2}
- (3^{ - 1} × 9^{ - 1}) ÷ 3^{ - 2}
- (11^{ - 1} + 12^{ - 1} + 13^{ - 1})^{0}
Answer
- (4^{0} + 4^{ - 1}) × 2^{2}
= (1+1/4) × 4
= 4+1=5
- (3^{ - 1} × 9^{ - 1}) ÷ 3^{ - 2}
= [(1/3) × (1/9)] ÷ (1/9)
=1/3
3. (11
^{ - 1} + 12
^{ - 1} + 13
^{ - 1})
^{0}
=1 as a
^{0 }=1
Question 4
Find the value of x here
(11/9)
^{3} x (9/11)
^{6} = (11/9)
^{2x-1}
Answer
(11/9)
^{3} x (11/9)
^{-6} = (11/9)
^{2x-1}
(11/9)
^{3-6} = (11/9)
^{2x-1}
-3=2x-1
Or
x=-1
Question 5
Find the value of
m for which 2
^{m} ÷ 2
^{-4} = 4
^{5}
Answer
2
^{m} ÷ 2
^{-4} = 4
^{5}
2
^{m} × (1/2
^{-4}) = 2
^{10}
2
^{m+4} =2
^{10}
So m+4=10
m=6
Question 6
Express the following numbers in standard form.
(i) 0.0000000015 (ii) 0.00000001425
(iii) 102000000000000000
Answer
- 0.0000000015
=1.5 ×10^{-9}
- 0.00000001425
=1.425×10^{-8}
3. 102000000000000000
=1.02×10
^{17}
Question 7
Express the following numbers in usual form.
(i) 34.02 x 10
^{-5} (ii) 9.5 x 10
^{5}
(iii) 9 x 10
^{-4} (iv) 2.0001 x 10
^{8}
Answer
- 34.02 x 10^{-5}
= .0003402
2. 9.5 x 10
^{5}
=950000
3. 9 x 10
^{-4}
=.0009
4. 2.0001 x 10
^{8}
=200010000
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