Question

If $216=2^a{3}^b$, then find the value of $a+b$.

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

Answer: (D)

$6$

$216=2^a{3}^b$ ...(1)

And, $216=6^3$ ...(2)

$\therefore 2^a{3}^b=6^3$ ....From (1) and (2)

$2^a\times 3^b=2^3\times 3^3$

So, $a=3,b=3$

$\therefore a+b=3+3=6$