# [C (gcc)], <sup><s>110</s> \$\cdots\$ <s>95</s></sup> 84 bytes
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d;p;r;f(a,l)int*a;{for(r=p=1;l--;r*=pow(p,*a++))for(d=2;d>1;)for(d=++p;p%--d;);d=r;}
[Try it online!][TIO-klxvzlsq]
[C (gcc)]: https://gcc.gnu.org/
[TIO-klxvzlsq]: https://tio.run/##3ZRtjpswEIb/5xQjJCRsjBq@oV62P6qeYhOtEJhdtGyCINJGjbh66YAdIFZP0Ahn4vfxjOMZM4XzVhTjWPKWd7yyctaQ@nShOb9V587qsjZzeeM4vKNZe/6yWkZz2yZkgmXm8fLZ5Wpi2y1vTccpOeFl1vFhbDsMZeEAmjOYbENgiguzWEMGe47mCRoOtl0TmD0qyzB7szQYLsuyPfwAw4DvgHODMMhf6iPhw@4zr08W2d12gJ8p3EX0l9f9yxGj3lwG6zPwlbuS77eap3y2mi81n4G3lQPlPgd@IOFC/pvnISGRPF@kHTte8h1v5UTKoSanajUGDwd@rxydYS@ZrCJT1VLWU9ZXNlA2VDZSNlY2UTZdNwGpNHKXvv4tzpUlNyPf1JSqOYMtdzXuatzTuKdxX@O@xgONBxoPNR5qPNJ4pPFY47HGE40nGk81npJNVsW1FcVFlDKtHvVpSGPqyjcPyxZPA8vkB1ibMMZCBX6M5YvSNEHjBUnieype8Z53FL9F8SE6GdA4XH95h2v6E0c4NYDN3DeU39pQTqW4qqYy/3y6H@T@N9ejLMrceabV2JrmcOutxFDyZs78yLcYGkXxSv0L94gxgdhOH3WB@pI03VE2zEene0sE5xnMEsz@cMJE9GxJVJ9l4qgcht0w/imqJn/rR@drdJrPvw "C (gcc) – Try It Online"
Inputs an array of prime exponents and its length \$l\$ and returns the product of the first \$l\$ primes to those exponents.
### Explanation
d;p;r;f(a,l)int*a;{ // function taking an array of
// ints and its length l
for(r=p=1;l--; // loop over the array elements
// setting the product r and
// the previous prime to 1
r*=pow(p,*a++) // once we've found the next
// prime multiply r by it
// to the power of the current
// value in a
for(d=2;d>1;) // loop until we find the next
// prime, d==1 will flag this
for(d=++p; // set d to p bumped
p%--d;) // bump d down and loop
// until we find the highest
// divisor of p
d=r; // return r
} //