Convert 0.8671875 to base 8 and base 16.

$$
0.8671875 \times 8 = 6.9375
$$
The integer part is 6. The new fractional part is 0.9375.

$$
0.9375 \times 8 = 7.5
$$
The integer part is 7. The new fractional part is 0.5.

$$
0.5 \times 8 = 4.0
$$
The integer part is 4. The new fractional part is 0.0.  
Since the fractional part is 0, we stop.  
Reading the integer parts from top to bottom gives the base 8 representation.
$$
0.8671875_{10} = \boxed{0.674_8}
$$

$$
0.8671875 \times 16 = 13.875
$$
The integer part is 13 (which is D in hexadecimal). The new fractional part is 0.875.

$$
0.875 \times 16 = 14.0
$$
The integer part is 14 (which is E in hexadecimal). The new fractional part is 0.0.  
Since the fractional part is 0, we stop.  
Reading the integer parts from top to bottom gives the base 16 representation.
$$
0.8671875_{10} = \boxed{0.\text{DE}_{16}}
$$

$$
0.53515625 \times 8 = 4.28125
$$
The integer part is 4. The new fractional part is 0.28125.

$$
0.28125 \times 8 = 2.25
$$
The integer part is 2. The new fractional part is 0.25.

$$
0.25 \times 8 = 2.0
$$
The integer part is 2. The new fractional part is 0.0.  
Since the fractional part is 0, we stop.
$$
0.53515625_{10} = \boxed{0.422_8}
$$

$$
0.53515625 \times 16 = 8.5625
$$
The integer part is 8. The new fractional part is 0.5625.

$$
0.5625 \times 16 = 9.0
$$
The integer part is 9. The new fractional part is 0.0.  
Since the fractional part is 0, we stop.
$$
0.53515625_{10} = \boxed{0.89_{16}}
$$

$$
0.626953125 \times 8 = 5.015625
$$
The integer part is 5. The new fractional part is 0.015625.

$$
0.015625 \times 8 = 0.125
$$
The integer part is 0. The new fractional part is 0.125.

$$
0.125 \times 8 = 1.0
$$
The integer part is 1. The new fractional part is 0.0.  
Since the fractional part is 0, we stop.
$$
0.626953125_{10} = \boxed{0.501_8}
$$

$$
0.626953125 \times 16 = 10.03125
$$
The integer part is 10 (which is A in hexadecimal). The new fractional part is 0.03125.

$$
0.03125 \times 16 = 0.5
$$
The integer part is 0. The new fractional part is 0.5.

$$
0.5 \times 16 = 8.0
$$
The integer part is 8. The new fractional part is 0.0.  
Since the fractional part is 0, we stop.
$$
0.626953125_{10} = \boxed{0.\text{A08}_{16}}
$$