Question

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

Answer 1

We know that $x^m\times x^n=x^{(m+n)}$ so simplifying using this as below

$(5^3\times 5^4\times 5^5\times 5^6)=5^{(3+4+5+6)}=5^{18}$

and

$(5^7\times 5^8)=5^{(7+8)}=5^{15}$

$5^{18}>5^{15}$

so, $(5^3\times 5^4\times 5^5\times 5^6)>(5^7\times 5^8)$