Question

If 2^a×3^b=576 then a/b

Answer 1

Answer:

3

Explanation:

576 = 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 = 2^6 * 3^2

=> 2^a * 3^b = 2^6 * 3^2

=> a = 6, b = 2

a/b = 6/2 = 3

Answer 2

Step-by-step explanation:

$576 =2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \\ \\ {2}^{a} \times {3}^{b} = 576 \\ {2}^{6} \times {3}^{2} = 576 \\ 64 \times 9 = 576 \\ \underline{ \underline{ 576 = 576}} \\ \\ \therefore \: \: a = 6 \: \: ; \: \: b = 2 \\ \\ \frac{a}{b} \\ = \frac{6}{2} \\ = \underline{\underline{\bf 3}}$