Question

without evaluating the expressions, tell which is greater, (4^4)(5^4) or (2^5)(10^5) . explain

Answer 1

$4^4\cdot5^4=20^4\\ 2^5\cdot10^5=20^5\\\\ 20^5>20^4 \implies 2^5\cdot10^5 > 4^4\cdot5^4$

Answer 2

There is more than one way to respond here.

I chose to leave (4^4)(5^4) as is and focus on finding an equivalent or two to

(2^5)(10^5). Note that (2^5)(10^5) factors as follows: (2^5)([2^5*5^5], or (2^5)*(2^5)*5^5

which in turn is equivalent to (2^10)*(5^5). Comparing this result to the original (4^4)(5^4), it's obvious that (2^5)(10^5) and its equivalents are larger than (4^4)(5^4).