Evaluatei 3-4ii -43iii 34-2iv -23-5v 570

(i) 3 4=134=181 (ii) 43= 13 #215;43= 1 #215;64= 64 (iii) 34 2=432=4232=169 (iv) 23 5=3 25=35 25=243 32=243 #215; 1 32 #215; 1= 24332 (v) Using the ...

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Byju's Answer

Standard VIII

Mathematics

Properties of Multiplication of Integers

Evaluatei 3-4...

Question

Evaluate:
(i) 3⁻⁴
(ii) (−4)³
(iii) ${(\frac{3}{4})}^{- 2}$
(iv) ${(\frac{- 2}{3})}^{- 5}$
(v) ${(\frac{5}{7})}^{0}$

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Solution

(i) $3^{- 4} = \frac{1}{3^{4}} = \frac{1}{81}$

(ii) ${(- 4)}^{3} = {(- 1)}^{3} \times {(4)}^{3} = - 1 \times 64 = - 64$

(iii) ${(\frac{3}{4})}^{- 2} = {(\frac{4}{3})}^{2} = \frac{4^{2}}{3^{2}} = \frac{16}{9}$

(iv) ${(\frac{- 2}{3})}^{- 5} = {(\frac{3}{- 2})}^{5} = \frac{3^{5}}{- 2^{5}} = \frac{243}{- 32} = \frac{243 \times - 1}{- 32 \times - 1} = \frac{- 243}{32}$

(v) Using the property ${(\frac{a}{b})}^{0} = 1$ , we have:
${(\frac{5}{7})}^{0} = 1$

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Evaluate: (i) 3−4 (ii) (−4)3 (iii) 34-2 (iv) -23-5 (v) 570

(i) 3-4=134=181 (ii) -43=-13×43=-1×64=-64 (iii) 34-2=432=4232=169 (iv) -23-5=3-25=35-25=243-32=243×-1-32×-1=-24332 (v) Using the property ab0=1, we have: 570 = 1

Evaluate:
(i) 3⁻⁴
(ii) (−4)³
(iii) ${(\frac{3}{4})}^{- 2}$
(iv) ${(\frac{- 2}{3})}^{- 5}$
(v) ${(\frac{5}{7})}^{0}$