Question
Download Solution PDFWhat is the digit in the units place of the number (1624)24?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Number = (1624)24
Formula Used:
The digit in the units place of a power of a number depends only on the digit in the units place of the base.
The cycle of the units digits for powers of 4 is:
41 = 4
42 = 16 (units digit is 6)
43 = 64 (units digit is 4)
44 = 256 (units digit is 6)
The pattern of the units digit of powers of 4 is 4, 6, 4, 6, ...
If the exponent is odd, the units digit is 4.
If the exponent is even, the units digit is 6.
Calculation:
The units digit of the base (1624) is 4.
The exponent is 24, which is an even number.
According to the pattern of the units digits for powers of 4, when the exponent is even, the units digit of the result is 6.
Therefore, the units digit of (1624)24 is 6.
∴ The digit in the units place of the number (1624)24 is 6.
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