Question

If $9000=5^a\times a^b\times b^a$, then find the value of $a^a+b^b$.

• A. $10$
• B. $31$
• C. $81$
• D. $85$

Answer 1

The correct option is B $31$

We can factorize $9000$ as $2\times 2\times 2\times 5\times 5\times 5\times 3\times 3=5^3\times 3^2\times 2^3$

$5^3\times 3^2\times 2^3$ = $5^a\times a^b\times b^a$

So, $a=3$ and $b=2$

We have to find out the value of $a^a+b^b$

$=3^3+2^2$

$=27+4=31$