To find the unit digit of the expression (37)^23 - (29)^37, we only need to consider the unit digit of each base, raised to the power of the exponent.

Step 1: Consider the unit digit of the base 37, which is 7. The cycle of unit digits for 7 raised to successive powers is 7, 9, 3, 1, repeating every 4 powers. So, to find the unit digit of 7^23, we find the remainder when 23 is divided by 4, which is 3. Therefore, the third number in the cycle, 3, is the unit digit of 7^23.

Step 2: Consider the unit digit of the base 29, which is 9. The cycle of unit digits for 9 raised to successive powers is 9, 1, repeating every 2 powers. So, to find the unit digit of 9^37, we find the remainder when 37 is divided by 2, which is 1. Therefore, the first number in the cycle, 9, is the unit digit of 9^37.

Step 3: Subtract the unit digit of 9^37 from the unit digit of 7^23, i.e., 3 - 9. Since we can't subtract a larger number from a smaller one, we add 10 to the smaller number before subtracting. So, 13 - 9 = 4.

Therefore, the unit digit of the expression (37)^23 - (29)^37 is 4.

Question

To find the unit digit of the expression (37)^23 - (29)^37, we only need to consider the unit digit of each base, raised to the power of the exponent.

Step 1: Consider the unit digit of the base 37, which is 7. The cycle of unit digits for 7 raised to successive powers is 7, 9, 3, 1, repeating every 4 powers. So, to find the unit digit of 7^23, we find the remainder when 23 is divided by 4, which is 3. Therefore, the third number in the cycle, 3, is the unit digit of 7^23.

Step 2: Consider the unit digit of the base 29, which is 9. The cycle of unit digits for 9 raised to successive powers is 9, 1, repeating every 2 powers. So, to find the unit digit of 9^37, we find the remainder when 37 is divided by 2, which is 1. Therefore, the first number in the cycle, 9, is the unit digit of 9^37.

Step 3: Subtract the unit digit of 9^37 from the unit digit of 7^23, i.e., 3 - 9. Since we can't subtract a larger number from a smaller one, we add 10 to the smaller number before subtracting. So, 13 - 9 = 4.

Therefore, the unit digit of the expression (37)^23 - (29)^37 is 4.

Knowee AI · Accepted Answer

To find the unit digit of the expression (37)^23 - (29)^37, we only need to consider the unit digit of each base, raised to the power of the exponent.

Step 1: Consider the unit digit of the base 37, which is 7. The cycle of unit digits for 7 raised to successive powers is 7, 9, 3, 1, repeating every 4 powers. So, to find the unit digit of 7^23, we find the remainder when 23 is divided by 4, which is 3. Therefore, the third number in the cycle, 3, is the unit digit of 7^23.

Step 2: Consider the unit digit of the base 29, which is 9. The cycle of unit digits for 9 raised to successive powers is 9, 1, repeating every 2 powers. So, to find the unit digit of 9^37, we find the remainder when 37 is divided by 2, which is 1. Therefore, the first number in the cycle, 9, is the unit digit of 9^37.

Step 3: Subtract the unit digit of 9^37 from the unit digit of 7^23, i.e., 3 - 9. Since we can't subtract a larger number from a smaller one, we add 10 to the smaller number before subtracting. So, 13 - 9 = 4.

Therefore, the unit digit of the expression (37)^23 - (29)^37 is 4.

Find the unit digit of the expression (37)23 – (29)37. Options 8 5 4 6

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