Question

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

Answer 1

a),108×192=2 power 8×3 power 4
b)270=3 cube ×2×5
C)729×64=2 power 6 ×3 power 6
d)768=2 power 8 ×3

Answer 2

a)  $108\times 192=2^8\times 3^4$

b) $270= 2\times 3^3\times 5$

c) $729\times 64= 3^6\times 2^6$

d) $768= 2^8\times 3$

Step-by-step explanation:

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

Solution :

a) $108\times 192$

Factor the numbers,

$108\times 192=(2\times 2\times3\times3\times3)\times (2\times 2\times2\times2\times 2\times2\times3)$

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

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

$108\times 192= 2^6 + 2\times3^3 + 1$

$108\times 192=2^8\times 3^4$

b) 270

Factor the number,

$270= 2\times 3\times 3\times 3\times 5$

$270= 2\times 3^3\times 5$

c) 729\times 64

Factor the number,

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

$729\times 64= 3^6\times 2^6$

d) 768

Factor the number,

$768= 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3$

$768= 2^8\times 3$

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