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nuccioreggie one year ago Which expression is equivalent to 73 ⋅ 7−5? 72 77 1 over 7 to the 2nd power 1 over 7 to the 7th power

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1. nuccioreggie

@Michele_Laino

2. tkhunny

Show your work. Don't forget your Order of Operations.

3. anonymous

So $\large7^3*\large7^{-5}$?

4. anonymous

Hello? @nuccioreggie

5. nuccioreggie

Ok 1sec

6. nuccioreggie

Yea thats the question

7. anonymous

$\Large7^3*\Large7^{-5}=\Large7^{3-5}$

8. nuccioreggie

I think the answer is B

9. anonymous

And why do you think that?

10. nuccioreggie

Idk

11. mathstudent55

To multiply powers with the same base, give the same base and add the exponents. Examples: $$\large 5^8 \cdot 5^7 = 5^{8 + 7} = 5^{15}$$ $$\large 3^{-5} \cdot 3^4 = 3^{-5 + 4} = 3^{-1}$$

12. mathstudent55

Also, after you multiply the powers together using the rule above, you need to know what to do with a negative exponent. For that use this rule: $$\large a^{-n} = \dfrac{1}{a^n}$$ Example: $$\large 5^{-3} = \dfrac{1}{5^3} = \dfrac{1}{125}$$

13. nuccioreggie

Ok i just did that and i got the answer choice

14. nuccioreggie

A

15. mathstudent55

First, multiply the powers together. The base is 7. What do you get for the exponent?

16. mathstudent55

What is 3 + (-5) = ?

17. nuccioreggie

-2

18. nuccioreggie

Sorry if i typee the same thing twice its not moe its my computer

19. mathstudent55

Good. So far you are correct. |dw:1433878869336:dw|

20. mathstudent55

Now you need to deal with the negative exponent. See my example above. A negative exponent ends up as a fraction.

21. nuccioreggie

Ohhhhh ok so its C

22. mathstudent55

Correct! |dw:1433878981234:dw|

23. nuccioreggie

Ok thanks can you help me with 2 more only please

24. tkhunny

And let's work on that notation. 73 ⋅ 7−5 = 73*7 - 5 = 511 - 5 = 506 Find SOME way to indicate an exponent. 7^3 * 7^(-5) Perhaps.

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