Evaluate-i 532 - 532ii 566 - 56-4iii 23-3-23-2iv 98-3 - 982

(i) 532 #215;532= #160;534=5434=62581 (ii) 566 #215;56 4=56(6+( 4))= #160;56(6 4)=562=5262=2536 (iii)23 3 #215;23 2=23( 3 2)=23 5=325=3525=24332 (i ...

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Byju's Answer

Standard VIII

Mathematics

Properties of Multiplication of Integers

Evaluate:i 53...

Question

Evaluate:
(i) ${(\frac{5}{3})}^{2} \times {(\frac{5}{3})}^{2}$
(ii) ${(\frac{5}{6})}^{6} \times {(\frac{5}{6})}^{- 4}$
(iii) ${(\frac{2}{3})}^{- 3} \times {(\frac{2}{3})}^{- 2}$
(iv) ${(\frac{9}{8})}^{- 3} \times {(\frac{9}{8})}^{2}$

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Solution

(i) ${(\frac{5}{3})}^{2} \times {(\frac{5}{3})}^{2} = {(\frac{5}{3})}^{4} = \frac{5^{4}}{3^{4}} = \frac{625}{81}$

(ii) ${(\frac{5}{6})}^{6} \times {(\frac{5}{6})}^{- 4} = {(\frac{5}{6})}^{(6 + (- 4))} = {(\frac{5}{6})}^{(6 - 4)} = {(\frac{5}{6})}^{2} = \frac{5^{2}}{6^{2}} = \frac{25}{36}$

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

(iv) ${(\frac{9}{8})}^{- 3} \times {(\frac{9}{8})}^{2} = {(\frac{9}{8})}^{(- 3 + 2)} = {(\frac{9}{8})}^{- 1} = \frac{8}{9}$

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Similar questions

Evaluate:

$(i) 5^{- 2} (i i) (- 3)^{- 2} (i i i) {(\frac{1}{3})}^{- 4} (i v) {(\frac{- 1}{2})}^{- 1}$

Now do these also:

(i) 3 + (−1)

(ii) 5 + (−4)

(iii)12 + (−2)

(iv) 8 + (−9)

(v) 9 + (−12)

(vi)

Q. Evaluate:
(i)

{(\frac{5}{9})}^{- 2} \times {(\frac{3}{5})}^{- 3} \times {(\frac{3}{5})}^{0}

(ii)

{(\frac{- 3}{5})}^{- 4} \times {(\frac{- 2}{5})}^{2}

(iii)

{(\frac{- 2}{3})}^{- 3} \times {(\frac{- 2}{3})}^{- 2}

Q. Evaluate:
(i)

2^{3} \times 4^{2}

(ii)

2^{3} \times 5^{2}

Q. 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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Evaluate: (i) 532×532 (ii) 566×56-4 (iii) 23-3×23-2 (iv) 98-3×982

(i) 532×532= 534=5434=62581 (ii) 566×56-4=56(6+(-4))= 56(6-4)=562=5262=2536 (iii)23-3×23-2=23(-3-2)=23-5=325=3525=24332 (iv) 98-3×982=98(-3+2)=98-1=89

Evaluate:
(i) ${(\frac{5}{3})}^{2} \times {(\frac{5}{3})}^{2}$
(ii) ${(\frac{5}{6})}^{6} \times {(\frac{5}{6})}^{- 4}$
(iii) ${(\frac{2}{3})}^{- 3} \times {(\frac{2}{3})}^{- 2}$
(iv) ${(\frac{9}{8})}^{- 3} \times {(\frac{9}{8})}^{2}$