# Math Gr. 9

a) Evaluate each power 3^1, 3^2, 3^4, 3^5, 3^6
b) Examine the final digit of each of your answers. What pattern do you notice?
c)Use the pattern you found in part b) to determine the final digit in the number 3^3234. Explain.

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3. 👁 157
1. Have you done step a?

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2. Yes, i got 3, 9,27,81, 243,729.

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3. Good.

Now for part b).

The final digits are

3, 9, 7, 1, 3, 9

What pattern do you see?

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4. it is a repeated pattern. The last digits of the total repeat from 3,9,1,

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5. Right.

Now for the last step --

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6. I don't know how to do the last step.

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7. step c is the one im struggling with

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8. I'm stuck, too. Please check back to see if one of our math experts can help you.

Btw -- if you'd started with what you know, and then asked about step c), I wouldn't have even attempted an answer.

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9. aw, ok. thankyou though.

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10. well, there is a trick here:Notice when the power of 3 is even, ....

check 3^12 ends in 1
3^10 ends in 9
3^8 ends in 1
3^6 ends in 9
3^4 ends in 1
3^2 ends in 9
3^0 ends in 1
So it alternates. Here the power is 3234. so lets see how many even alterations. Answer, 3234/2=1617, an odd number. Start with the power of zero, any odd number of alterations of this power must end in 9.

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11. ohhhhhhhhh. thankyou so much ! you helped me alot !

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