Question

5. Acomposite number 144=2^a ×3^b then a+b=
a)6
b)5
c)12
d)7​

Answer 1

Answer:

a) 6

Step-by-step explanation:

144 = 2 × 2 × 2 × 2 × 3 × 3

$144 = {2}^{a} \times {3}^{b} \\ 144 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \\ 144 = {2}^{4} \times {3}^{2} \\ {2}^{a} \times {3}^{b} = {2}^{4} \times {3}^{2} \\ a = 4 \: \: \: \: b = 2 \\ a + b = 4 + 2 = 6$

hope you get your answer