Question

Which is larger: $(5^3\times 5^4\times 5^5\times 5^6)or(5^7\times 5^8)$?

Answer 1

By using $a^m\times a^n=a^{m+n}$, we get
$5^3\times 5^4\times 5^5\times 5^6=5^{3+4+5+6}$
$=5^{18}$
And $5^7\times 5^8=5^{7+8}$
$=5^{15}$
Since $18>15$
$\Rightarrow 5^{18}>5^{15}$

Therefore, $5^3\times 5^4\times 5^5\times 5^6>5^7\times 5^8$