##### Simplify and express each of the following in exponential form:(i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x) (xi) (xii)

(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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