Write some code that takes a single non-negative integer \$n\$ and outputs the \$n\$th power of phi (\$\phi\$, the Golden Ratio, approximately 1.61803398874989) with the same number of decimal digits as the \$n\$th Fibonacci number.
Your code must produce the correct sequence of digits for all inputs up to at least 10 (55 decimal digits). The output must be human-readable decimal. You may choose whether to round the last digit to the closest value, or truncate the value. Please specify which one your code uses.
\$n\$ and output, up to 10, rounding down:
0 1
1 1.6
2 2.6
3 4.23
4 6.854
5 11.09016
6 17.94427190
7 29.0344418537486
8 46.978713763747791812296
9 76.0131556174964248389559523684316960
10 122.9918693812442166512522758901100964746170048893169574174
\$n\$ and output, up to 10, rounding to the closest value:
0 1
1 1.6
2 2.6
3 4.24
4 6.854
5 11.09017
6 17.94427191
7 29.0344418537486
8 46.978713763747791812296
9 76.0131556174964248389559523684316960
10 122.9918693812442166512522758901100964746170048893169574174
The 7th Fibonacci number is 13, so the output for \$n=7\$, \$\phi^7\$, has 13 decimal places. You must not truncate trailing zeros that would display too few digits; see output for 6 in the first table, which ends in a single zero to keep the decimal precision at 8 digits.
Maybe as a bonus, say what the highest number your program can correctly output is.