C (gcc), ^{(削除) 110 (削除ここまで) \$\cdots\$ (削除) 84 (削除ここまで)} 79 bytes

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d;p;r;f(a,l)int*a;{for(r=p=1;l;r*=pow(p,d<2?l--,*a++:0))for(d=++p;p%--d;);d=r;}

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C (gcc), ^{(削除) 110 (削除ここまで) \$\cdots\$ (削除) 79 (削除ここまで)} 75 bytes

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d;p;r;f(a,l)int*a;{for(r=p=1;l;r*=pow(p,d<2?l--,*a++:0))for(d=++p;p%--d;);}

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C (gcc), ^{(削除) 110 (削除ここまで) \$\cdots\$ (削除) 95 (削除ここまで)} 84 bytes

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;}

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Explanation

C (gcc), ^{(削除) 110 (削除ここまで) \$\cdots\$ (削除) 84 (削除ここまで)} 79 bytes

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d;p;r;f(a,l)int*a;{for(r=p=1;l;r*=pow(p,d<2?l--,*a++:0))for(d=++p;p%--d;);d=r;}

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Explanation (before some golfs)

Inputs an array of prime exponents and its length \$l\$ and returns the product of the first \$l\$ primes to those exponents.

Inputs an array of prime exponents and its length \$l\$ (because C arrays have undefined length) and returns the product of the first \$l\$ primes to those exponents.