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Quantity A: The units digit of 13 × 13¹³ Quantity B: The units digit of 19 × 19¹⁹ A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.

1 Answer

5 votes

The units digit of Quantity A is 9.

The units digit of Quantity B is 1 (the units digit of 81).

Therefore, Quantity B is greater than Quantity A.

Quantity A:

The units digit of 13 is 3.

The units digit of powers of 3 follow a cycle of 4: {3, 9, 7, 1}.

Since 13 is odd, 13¹³ will also have the same units digit as 3¹³.

Therefore, the units digit of 13 × 13¹³ is the product of the units digits of 3 and 3¹³, which is 3 * 3 = 9.

Quantity B:

The units digit of 19 is 9.

Similar to Quantity A, the units digit of powers of 9 follow a cycle of 2: {9, 1}.

Since 19 is odd, 19¹⁹ will also have the same units digit as 9¹⁹.

Therefore, the units digit of 19 × 19¹⁹ is the product of the units digits of 9 and 9¹⁹, which is 9 * 9 = 81.

answered
User Jonathan Hersh
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