BUG #17546: power() function - value is distorted via automatic type cast

The following bug has been logged on the website:

Bug reference: 17546
Logged by: Su Sinodan
Email address: su(dot)sinodan(at)gmail(dot)com
PostgreSQL version: 14.2
Operating system: Windows Server 2016 (10.0.14393 Build 1439)
Description:

When a certain number (p, s) with a fractional part (specific examples -
1.11 and 69.96) is multiplied by a power (10, N), the resulting value is
distorted.
However, if the power(10, N) is manually converted to an integer, the
resulting value is correct.
It looks like there is some kind of problem with the automatic type
conversion of the power() function.

Test query:
with w_degree as (
select 0::integer as degree union all
select 1::integer as degree union all
select 2::integer as degree union all
select 3::integer as degree union all
select 4::integer as degree union all
select 5::integer as degree union all
select 6::integer as degree union all
select 7::integer as degree union all
select 8::integer as degree union all
select 9::integer as degree
)
select
power(10, w.degree::integer) as
"power()"
, 1.11::numeric(20, 5) * power(10, w.degree::integer) as " 1.11 *
power()"
, 1.11::numeric(20, 5) * power(10, w.degree::integer)::integer as " 1.11 *
power()::integer"
, 69.96::numeric(20, 5) * power(10, w.degree::integer) as "69.96 *
power()"
, 69.96::numeric(20, 5) * power(10, w.degree::integer)::integer as "69.96 *
power()::integer"
from w_degree w;

Result:
power() | 1.11 * power() | 1.11 * power()::integer | 69.96 *
power() | 69.96 * power()::integer
------------+--------------------+--------------------------+-------------------+--------------------------
1 | 1.11 | 1.11000 |
69.96 | 69.96000
10 | 11.100000000000001 | 11.10000 |
699.5999999999999 | 699.60000
100 | 111.00000000000001 | 111.00000 |
6995.999999999999 | 6996.00000
1000 | 1110 | 1110.00000 |
69960 | 69960.00000
10000 | 11100.000000000002 | 11100.00000 |
699599.9999999999 | 699600.00000
100000 | 111000.00000000001 | 111000.00000 |
6995999.999999999 | 6996000.00000
1000000 | 1110000 | 1110000.00000 |
69960000 | 69960000.00000
10000000 | 11100000.000000002 | 11100000.00000 |
699599999.9999999 | 699600000.00000
100000000 | 111000000.00000001 | 111000000.00000 |
6995999999.999999 | 6996000000.00000
1000000000 | 1110000000 | 1110000000.00000 |
69960000000 | 69960000000.00000
(10 rows)