Question

Simplify the following by converting into exponential form: $\frac{36*9}{12*4}$

Answer 1

6^ 2* 3^2/ 12* 2^ 2

Is that correct?? not sure

Answer 2

Solution :

2 | 36
_______
2 | 18
_______
3 | 9
_______
*****3

36 = 2² × 3²

9 = 3² ,

12 = 2² × 3 ,

4 = 2²

Given ( 36 × 9 )/( 12 × 4 )

= ( 2² × 3² × 3² )/( 2² × 3¹ × 2² )

= ( 2² × 3^2+2 )/( 2^2+2 × 3¹ )

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We know the Exponential laws :

i ) a^m × a^n = a^m+n

ii ) a^m/a^n = a^m-n

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= ( 2² × 3⁴ )/( 2⁴ × 3¹ )

= ( 3^4-1 )/( 2^4-2 )

= 3³/2²

= 27/4

Therefore ,

( 36 × 9 )/( 12 × 4 ) = 27/4

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