In this page we have NCERT book Solutions for Class 8th Maths Chapter 12:Exponents and Power for
Exercise 12.1 . Hope you like them and do not forget to like , social share
and comment at the end of the page.
Question 1
Evaluate
(i) $3^{-2}$
(ii) $(-4)^{-2}$
(iii)$(\frac {1}{2})^{-5}$
Answer
As we know that
$b^{-n}= \frac {1}{b^n}$
(i) $3^{-2}=\frac {1}{3^2} =\frac {1}{9}$
(ii) $(-4)^{-2}=\frac {1}{(-4)^2}= \frac {1}{16}$
(iii) $(\frac {1}{2})^{-5}=\frac {1}{2^{-5}}=2^5= 32$
Question 2
Simplify and express the result in power notation with positive exponent.
Answer
(i)
= (-4)
^{5} / (-4)
^{8}
= (-4)
^{5-8}
=1/ (-4)
^{3}
(ii)
= 1/2
^{3x2}
=1/2
^{6}
(iv )
= (3
^{-7}/ 3
^{-10}) × 3
^{-5}
=3
^{-7+10} × 3
^{-5}
=3
^{3} × 3
^{-5}
=3
^{-2}
=1/3
^{2}
(v) 2
^{ - 3} × ( - 7)
^{ - 3}
= (2× -7)
^{-3}
= (-14)
^{-3}
=1/ (-14)
^{3}
Question 3
Find the value of
- (3^{0} + 4^{ - 1}) × 2^{2}
- (2^{ - 1} × 4^{ - 1}) ÷ 2^{ - 2}
- $(\frac {1}{2})^{-2} + (\frac {1}{3})^{-2} + (\frac {1}{4})^{-2}$
- (3^{ - 1} + 4^{ - 1} + 5^{ - 1})^{0}
- $\left \{ \left (\frac {-2}{3 }\right )^{-2} \right \}^2$
Answer
1.(3
^{0} + 4
^{ - 1}) × 2
^{2}
= (1+1/4) × 4
= 4+1=5
2. (2
^{ - 1} × 4
^{ - 1}) ÷ 2
^{ - 2}
= [(1/2) × (1/4)] ÷ (1/4)
= (1/8) × (4) =1/2
3.
$(\frac {1}{2})^{-2} + (\frac {1}{3})^{-2} + (\frac {1}{4})^{-2}$
= 2
^{2} + 3
^{2 } + 4
^{2}
=4+9+16=29
4. (3
^{ - 1} + 4
^{ - 1} + 5
^{ - 1})
^{0}
=1 as a
^{0}=1
5.$\left \{ \left (\frac {-2}{3 }\right )^{-2} \right \}^2$
$=\left (\frac {-2}{3 }\right )^{-4}$
$=\frac {81}{16}$
Question 4
Evaluate
i. $ \frac {8^{-1} \times 5^3}{2^{-4}}$
ii. $(5^{-1} \times 2^{-1}) \times 6^{-1}$
Answer
i. $ \frac {8^{-1} \times 5^3}{2^{-4}}$
$=\frac {2^4 \times 5^3}{8} = 250$
ii. $(5^{-1} \times 2^{-1}) \times 6^{-1}$
$=( \frac {1}{5} \times \frac {1}{2} ) \times \frac {1}{6}$
$=\frac {1}{60}$
Question 5
Find the value of
m for which 5
^{m} ÷ 5
^{-3} = 5
^{5}
Answer
5
^{m} ÷ 5
^{-3} = 5
^{5}
5
^{m} × (1/5
^{-3}) = 5
^{5}
5
^{m+3} =5
^{5}
So m+3=5
m=2
Question 6
Evaluate
i. $\left \{ \left ( \frac {1}{3} \right )^{-1} - \left ( \frac {1}{4} \right )^{-1} \right \}^{-1}$
ii. $\left ( \frac {5}{8} \right )^{-7} \times \left ( \frac {8}{5} \right )^{-4}}$
Answer
i. $\left \{ \left ( \frac {1}{3} \right )^{-1} - \left ( \frac {1}{4} \right )^{-1} \right \}^{-1}$
$={3^2 - 4^1}^{-1} = -1$
ii. $\left ( \frac {5}{8} \right )^{-7} \times \left ( \frac {8}{5} \right )^{-4}}$
$=\left ( \frac {5}{8} \right )^{-7} \times \left ( \frac {5}{8} \right )^{4}}$
$=\left ( \frac {5}{8} \right )^{-3}= \frac {512}{125}$
Question 7
Simplify.
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