# SOLUTION: find the units digit of 3^13*7^14 without actual multiplication

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 Question 60968: find the units digit of 3^13*7^14 without actual multiplicationAnswer by joyofmath(189)   (Show Source): You can put this solution on YOUR website!We're looking at Well, so ends in 3. ends in 3*3 or 9. ends in 9*3 =27 so it ends in 7. ends in 7*3 = 21 so it ends in 1. ends in 1*3 or 3. So it ends in the same as . ends in 3*3 ends the same as . ends in 9*3 ends the same as . So, the pattern repeats every 4 powers. So, ands with the same digit as and which is 3. ends in 7. ends in the same digit as 7*7, or 9. ends in the same digit as 9*7, or 3. ends in the same digit as 3*7, or 1. ends in the same digit as 1*7, which ends the same way as . So, this pattern also repeats every 4 powers. So, ends the same way as and and which is with a 9. So, ends with the same digit as which ends in 3 multiplied by the last digit of which is 9. So, the big product ends in so 7 is the last digit of the big product.