Question

Express each of the following as a product af prime factors only in exponential form
(plz answer correctly)
a-108 × 192
b-729 × 64
c-270
d-768

Answer 1

Answer:

a) 108\times 192=2^8\times 3^4108×192=2

8

×3

4

b) 270= 2\times 3^3\times 5270=2×3

3

×5

c) 729\times 64= 3^6\times 2^6729×64=3

6

×2

6

d) 768= 2^8\times 3768=2

8

×3

Step-by-step explanation:

To find : Express each of the following as a product of prime factors only in exponential form ?

Solution :

a) 108\times 192108×192

Factor the numbers,

108\times 192=(2\times 2\times3\times3\times3)\times (2\times 2\times2\times2\times 2\times2\times3)108×192=(2×2×3×3×3)×(2×2×2×2×2×2×3)

108\times 192= (2^2 \times 3^3)\times (2^6\times 3)108×192=(2

2

×3

3

)×(2

6

×3)

Using identity : a^m\times a^n = a^{m + n}a

m

×a

n

=a

m+n

108\times 192= 2^6 + 2\times3^3 + 1108×192=2

6

+2×3

3

+1

108\times 192=2^8\times 3^4108×192=2

8

×3

4

b) 270

Factor the number,

270= 2\times 3\times 3\times 3\times 5270=2×3×3×3×5

270= 2\times 3^3\times 5270=2×3

3

×5

c) 729\times 64

Factor the number,

729\times 64= (3\times 3\times 3\times 3\times 3\times 3)\times (2\times 2\times 2\times 2\times 2\times 2)729×64=(3×3×3×3×3×3)×(2×2×2×2×2×2)

729\times 64= 3^6\times 2^6729×64=3

6

×2

6

d) 768

Factor the number,

768= 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3768=2×2×2×2×2×2×2×2×3

768= 2^8\times 3768=2

8

×3