What is the value of 32_4 + 43_5 + 54_6 when written in base 7?
To simplify our calculations, we can rewrite each number in base 7 before adding them together.
For the first number, 32_4, we can convert it to base 7 by expanding the digits in powers of 7:
32_4 = (3 * 4^1) + (2 * 4^0) = 12 + 2 = 14_10 = 20_7
Similarly, for the second number, 43_5, we convert it to base 7:
43_5 = (4 * 5^1) + (3 * 5^0) = 20 + 3 = 23_10 = 32_7
For the third number, 54_6, we convert it to base 7:
54_6 = (5 * 6^1) + (4 * 6^0) = 30 + 4 = 34_10 = 43_7
Now, we add these numbers together in base 7:
20_7 + 32_7 + 43_7 = 95_7
Therefore, when written in base 7, the value of 32_4 + 43_5 + 54_6 is 95_7.