JavaScript, 51 bytes

f=(a,b,c,h,i,j)=>(l=Math.log)(a)*b**c-l(h)*i**j>0.01

Surprisingly, the test cases doesn't show any floating-point error. I don't know if it ever does at this size.

This just compares the logarithm of the numbers.

I don't know if the tolerance 0.01 should work for {a,b,c,h,i,j}⊂{1,2,...,20}.

JavaScript, 51 bytes

f=(a,b,c,h,i,j)=>(l=Math.log)(a)*b**c-l(h)*i**j>1e-8

Surprisingly, the test cases doesn't show any floating-point error. I don't know if it ever does at this size.

This just compares the logarithm of the numbers.

Equality tolerance is equal to 1e-8.

JavaScript, 47 bytes

f=(a,b,c,h,i,j)=>(l=Math.log)(a)/l(h)*b**c>i**j

Surprisingly, the test cases doesn't show any floating-point error. I don't know if it ever does at this size.

This just compares the logarithm of the numbers.

JavaScript, 51 bytes

f=(a,b,c,h,i,j)=>(l=Math.log)(a)*b**c-l(h)*i**j>0.01

Surprisingly, the test cases doesn't show any floating-point error. I don't know if it ever does at this size.

This just compares the logarithm of the numbers.

I don't know if the tolerance 0.01 should work for {a,b,c,h,i,j}⊂{1,2,...,20}.

JavaScript, 47 bytes

f=(a,b,c,h,i,j)=>(l=Math.log)(a)*b**c>l(h)*i**j

Surprisingly, the test cases doesn't show any floating-point error. I don't know if it ever does at this size.

This just compares the logarithm of the numbers.

JavaScript, 47 bytes

f=(a,b,c,h,i,j)=>(l=Math.log)(a)/l(h)*b**c>i**j

Surprisingly, the test cases doesn't show any floating-point error. I don't know if it ever does at this size.

This just compares the logarithm of the numbers.