Help w/ Math Destroyer Question!

[deleted667906]

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Simplify 2^15/ (8^3 + 4^3)

I used the common base of 2 and simplified to --> 2^15/ (2^9 +2^6)

I wasn't sure where to go from here so I took a look at the solutions and it said they next step was
2^15/ 2^6 (2^3 +1) --> 2^9/ 9

I don't understand how to get to this answer can anyone help me out?! Dr. Romano?

 

[BYU4you]

When you have common numbers like 2^15/2^6 just minus the bottom exponent from the top hence 2^9 is left on top and 2^6 is just one or left out in this case.

Then to get 9 on bottom your just working out the parenthesis, 2^3 is 8 and add one to get 9

If you were wondering, the bottom 2^6 was just factored out at the start

 

[DAT Destroyer]

Simplify 2^15/ (8^3 + 4^3)

I used the common base of 2 and simplified to --> 2^15/ (2^9 +2^6)

I wasn't sure where to go from here so I took a look at the solutions and it said they next step was
2^15/ 2^6 (2^3 +1) --> 2^9/ 9

I don't understand how to get to this answer can anyone help me out?! Dr. Romano?

In the denominator factor out 2^6 and you get :
2^15/2^6(2^3+1) then divide 2^15 by 2^6 and you get 2^9 in the numerator and (2^3+1) in the denominator which 2^9/9.
Another way:
When you get 2^15/(2^9+2^6) divide each term by 2^6 ( the smallest exponent) and you should get the same result.

 

[deleted667906]

Wow I don't know how I didn't see that before. Thanks for the help!

 

[DAT Destroyer]

Wow I don't know how I didn't see that before. Thanks for the help!

Glad I could help!