# Powered Up

Can you work out the product of these indices?

Given that $5^p = 9$, $9^q = 12$, $12^r = 16$, $16^s = 20$ and $20^t = 25$,

what is the value of $pqrst$?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

**Answer**: 2

$5^p = 9$ and $9^q = 12$.

Therefore $(5^p)^q = 12$, that is $5^{pq} = 12$.

Similarly, as $12^r = 16$ then $5^{pqr} = 16$

AsĀ $16^s = 20$ then $5^{pqrs} = 20$

As $20^t = 25$ then $5^{pqrst} = 25$.

Therefore $pqrst = 2$.