### Instruction: What is the units digit when $7^{53}$ is multiplied out?### Response: I know that the units digit of a power of 7 depends on the exponent, and it cycles through a pattern of 7, 9, 3, and 1 every four powers.
So, to find the units digit of $7^{53}$, I just need to figure out where 53 falls in that cycle.
I can divide 53 by 4 and get a quotient of 13 and a remainder of 1.
That means that 53 is one more than a multiple of 4, so it is the first power in the cycle.
Therefore, the units digit of $7^{53}$ is the same as the units digit of $7^1$, which is 7.