Exponential

$(4^x)(5^x)=(2^x)(7^x)$

$20^x=14^x$

We knew that if $a^n=b^n \Rightarrow a=b$ but $20 \not= 14$ . Therefore, the only answer here is $\boxed{0}$ .

If we expand, the equalty would be as next: 20^x=14^x. Since those numbers has different primes in their compositions, just one choice is left: picking 0 as an exponent, because every 0 exponential is 1. There, 0 is the answer

$(4^x)(5^x)=(2^x)(7^x) \implies{20^x=14^x} \implies{ \frac{(20^x)}{(14^x)}}=1 \implies {( \frac{20}{14})^x}=1$

Because $1= ( \frac{20}{14})^0,$ so we have,

${(\frac{20}{14})^x}={ ( \frac{20}{14})^0}$

Give us $x= \boxed 0$