Q. 24.3( 157 Votes )

Simplify and expr

Answer :

(i) In the above question,

We have to simplify the given numbers into exponential form:


We have,


=


=


=


= (am × an = am + n)


Using identity: (am an = am - n)


= 25 - 5 × 34 – 1


= 2033


= 1 × 33


= 33


(ii) In the above question,


We have to simplify the given numbers into exponential form:


[(52)3 × 54] 57


Using identity: (am)n = amn)


= [(5)2 × 3 × 54] 57


= [(5)6 × 4] 57


Using identity: (am × an = am + n)


= [56 + 4] 57


Using identity: (am an = am - n)


Therefore,


= 510 57


= 510 – 7


= 53


(iii) In the above question,


We have to simplify the given numbers into exponential form:


We have,


254 53


= (5 × 5)4 53


Using identity: (am)n = amn


= 52 × 4 53


= 58 53


Using identity: (am an = am - n)


58 53


= 58 – 3


= 55


(iv) In the above question,


We have to simplify the given numbers into exponential form:


We have,



=


Using identity: (am an = am - n)


= 31 - 1 × 72 – 1 × 118 – 3


= 30 × 71 × 115


= 1 × 7 × 115


= 7 × 115


(v) In the above question,


We have to simplify the given numbers into exponential form:


We have,



Using identity: (am × an = am + n)


=


Using identity (am an = am - n)


= 37 - 7


= 3o


= 1


(vi) In the above question,


We have to simplify the given numbers into exponential form:


We have,


20 + 30 + 40


= 1 + 1 + 1


= 3


(vii) In the above question,


We have to simplify the given numbers into exponential form:


We have,


20 × 30 × 40


= 1 × 1 × 1


= 1


(viii) In the above question,


We have to simplify the given numbers into exponential form:


We have,


(30 + 20) × 50


= (1 + 1) × 1


= 2


(ix) In the above question,


We have to simplify the given numbers into exponential form:


We have,



=


Using identity: (am)n = amn



Using identity: (am an = am - n)


= 28 – 6 × a5 - 3


= 22 × a2


Using identity [am ×bm = (a × b)m]


= (2 × a)2


= (2a)2


(x) In the above question,


We have to simplify the given numbers into exponential form:


We have,


() × a8


Using identity: (am an = am - n)


= a5 – 3 × a8


= a2 × a8


Using identity (am × an = am + n)


= a2 + 8


= a10


(xi) In the above question,


We have to simplify the given numbers into exponential form:


We have,



Using identity: (am an = am - n)


= 45 – 5 × a8 – 5 × b3 – 2


= 40 × a3 × b1


= 1 × a3 × b


= a3b


(xii) In the above question,


We have to simplify the given numbers into exponential form:


We have,


(23 × 2)2


Using identity: (am × an = am + n)


= (23 + 1)2


= (24)2


Using identity: (am)n = amn


Therefore,


= 24 × 2


= 28

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