Evaluate-i 3-2ii -4-2iii 12-5

(i) To evaluate: 3^ 2 Now, #160;3^ 2 = 13^2 =19 #160; Hence, the required value is 19 .(ii) #160; #160;To evaluate: ( 4)^ 2 Now, # ...

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Standard VIII

Mathematics

Power of a Power

Evaluate:i ...

Question

Evaluate:
(i) $3^{- 2}$
(ii) $(- 4)^{- 2}$
(iii) ${(\frac{1}{2})}^{- 5}$

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Solution

(i) To evaluate: $3^{- 2}$

Now,
$3^{- 2} = \frac{1}{3^{2}} = \frac{1}{9}$

Hence, the required value is $\frac{1}{9}$ .

(ii) To evaluate: $(- 4)^{- 2}$

Now,
$(- 4)^{- 2} = \frac{1}{(- 4)^{2}} = \frac{1}{4^{2}} = \frac{1}{16}$

Hence, the required value is $\frac{1}{16}$ .

(iii) To evaluate: ${(\frac{1}{2})}^{- 5}$

Now,
${(\frac{1}{2})}^{- 5} = \frac{1}{(2)^{- 5}} = 2^{5} = 32$

Hence, the required value is $32$ .

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Evaluate:(i) 3−2(ii) (−4)−2(iii) (12)−5

(i) To evaluate: 3−2Now,3−2=132=19Hence, the required value is 19 .(ii) To evaluate: (−4)−2Now,(−4)−2=1(−4)2=142=116Hence, the required value is 116 .(iii) To evaluate: (12)−5Now,(12)−5=1(2)−5=25=32Hence, the required value is 32 .

Evaluate:
(i) $3^{- 2}$
(ii) $(- 4)^{- 2}$
(iii) ${(\frac{1}{2})}^{- 5}$