## raphaelll one year ago Simplify the following expressions. Give your answers in power notation where the powers are positive. 8 to the power of -6 x 8 to the power of 2 6 to the power of 7 divided by 6 to the power of 12

1. zepdrix

So the first one is this, ya? $$\large\rm 5^5\cdot5^5$$

2. raphaelll

Yup thats the first one

3. zepdrix

Here is our rule of exponents that will be very helpful to use: $$\large\rm x^a\cdot x^b=x^{a+b}$$

4. zepdrix

Notice that when we apply this rule, the base stays the same.

5. zepdrix

Any ideas how we can use this? :)

6. raphaelll

umm, i just take 5 and add the two powers together?

7. zepdrix

$\large\rm 5^\color{orangered}{5}\cdot5^\color{orangered}{5}=5^{\color{orangered}{5+5}}$Mmm good!

8. raphaelll

thanks! how do i go about doing the second question since there is a negative power?

9. zepdrix

8 to the power of -6 x 8 to the power of 2 $\large\rm 8^{-6}\cdot8^{2}=8^{-6+2}$Same thing, addition :) Remember how to add a negative and positive together?

10. raphaelll

oh i see, is it also just addition if division is the middle step?

11. zepdrix

division is a little different: $$\large\rm x^a\div x^b=x^{a-b}$$

12. zepdrix

6 to the power of 7 divided by 6 to the power of 12 $\large\rm 6^7\div6^{12}=6^{7-12}$ Make sure you write the 7 and 12 in the correct locations. I was forced to write the 7 first because that shows up on the left of the division. The 7 is smaller, so yes, you should end up with a negative power after you complete the subtraction.

13. raphaelll

okay thank you! so for multiplication it is just adding the two powers, and for division it is subtracting the two powers

14. zepdrix

Yes! You might be able to see a connection between the multiplication and division... if you really think about it. Not a big deal though :)

15. raphaelll

you wouldn't happen to know anything about scientific notation would you? it's the last two questions on my assignment that i don't understand

16. zepdrix

Can you write out the question? :o That might make it easier for us.

17. raphaelll

26.9 x 463 000 and 55.18 divided by 620

18. zepdrix

For the first one, when you do the multiplication you get: $$\large\rm 12,454,700$$ This is not scientific notation. For scientific notation, we want to write this as a number... times some power of 10.

19. zepdrix

|dw:1441616656957:dw|So we want to write the number like this. The number that goes here $$\large\rm \square$$ should be a single digit. something larger than 1, and less than 10. So when we look at our number, we can see that THIS is the number that goes in the square:

20. zepdrix

|dw:1441616745335:dw|

21. zepdrix

I'm going to write a decimal after that number,|dw:1441616795550:dw|

22. zepdrix

The number that goes in the $$\large\rm \triangle$$ is the number of places that you moved the decimal.

23. zepdrix

|dw:1441616863094:dw|Decimal always starts here by the way.

24. zepdrix

|dw:1441616886977:dw|Looks like we had to move the decimal 7 places.

25. zepdrix

|dw:1441616919559:dw|Bam ok we got the first one done!

26. zepdrix

Any confusion there? :o

27. raphaelll

no actually you explained that really well!

28. zepdrix

55.18 divided by 620 This one is a little different... doing the division we end up with: $$\large\rm 0.089$$

29. zepdrix

So what number goes in the $$\large\rm \square$$, what do you think? :o

30. raphaelll

8 because it is greater than 1 but less than 10

31. zepdrix

Ok good! We want to keep all of the important values that follow the 8 as well.$\LARGE\rm 8.9\times10^?$

32. raphaelll

10 to the power of 3?

33. zepdrix

|dw:1441617458964:dw|Hmm, I don't think we moved 3 place values! :)

34. raphaelll

oh yup my bad, i looked at the diagram from before thinking the decimal started from the end

35. zepdrix

So, what's different about this problem is that ... since we're moving the decimal to the right, the exponent on the 10 will be negative.

36. raphaelll

okay so if the decimal is moved to the right it is negative whereas to the left is positive, so the answer is 10 to the power of 2

37. raphaelll

negative 2*

38. zepdrix

$\LARGE\rm 8.9\times10^{-2}$Yay good job team \c:/

39. raphaelll

thank you so much for all your help! will definitely be in touch if i ever need more help :P