Convert $135_7$ to a base 10 integer.
To convert a number from base 7 to base 10, I need to multiply each digit by its corresponding power of 7 and add up the results. The rightmost digit has a power of 7^0 = 1, the next one has a power of 7^1 = 7, and the leftmost one has a power of 7^2 = 49. So, $135_7 = 1 \times 49 + 3 \times 7 + 5 \times 1 = 49 + 21 + 5 = 75_{10}$. 