1052 toothpicks can be grouped into 4 groups of third power of 6 (
), 5 groups of second power of 6 (
), 1 group of first power of 6 (
) and 2 groups of zeroth power of 6 (
).
The number 1052, written as a base 6 number is 4512
Given: 1052 toothpicks
To do: The objective is to group the toothpicks in powers of 6 and to write the number 1052 as a base 6 number
First we note that, 
This implies that 
exceeds 1052 and thus the highest power of 6 that the toothpicks can be grouped into is 3.
Now, 
and 
. This implies that 
exceeds 1052 and thus there can be at most 4 groups of .
Then,
So, after grouping the toothpicks into 4 groups of third power of 6, there are 188 toothpicks remaining.
Now, 
and 
. This implies that 
exceeds 188 and thus there can be at most 5 groups of .
Then,
So, after grouping the remaining toothpicks into 5 groups of second power of 6, there are 8 toothpicks remaining.
Now, 
and 
. This implies that 
exceeds 8 and thus there can be at most 1 group of .
Then,
So, after grouping the remaining toothpicks into 1 group of first power of 6, there are 2 toothpicks remaining.
Now, 
and 
. This implies that the remaining toothpicks can be exactly grouped into 2 groups of zeroth power of 6.
This concludes the grouping.
Thus, it was obtained that 1052 toothpicks can be grouped into 4 groups of third power of 6 (), 5 groups of second power of 6 (), 1 group of first power of 6 () and 2 groups of zeroth power of 6 ().
Then,
So, the number 1052, written as a base 6 number is 4512.
Learn more about change of base of numbers here:
brainly.com/question/14291917
since dividing numbers with exponents would be subtracting the bottom exponent from the top exponent, provided that the base number (in this case 3) is the same for both. For this method, you would get 
, which is equal to 1/9 or .1 repeating, the same answer that you'd get with the first method.