From base seven to base ten

Statement

Convert the number $(2536)_7$ (written in base seven) to base ten.

Solution

Each digit carries a power of $7$: $(2536)_7 = 2\cdot 7^3 + 5\cdot 7^2 + 3\cdot 7 + 6.$ $= 2\cdot 343 + 5\cdot 49 + 21 + 6 = 686 + 245 + 21 + 6 = \boxed{958}.$