Math Destroyer Question Help

[snaggletoof]

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Having a problem understanding this question in Math Destroyer....

its practice test 7, question 32

Evaluate:

[8^6 - 4^7]/2^14

this is as far as I got:

8^6 = 2^3x6 = 2^18

4^7 = 2^2x7 = 2^14

so....

[2^18 - 2^14]/2^14

My logic would be to subtract the two exponents in the numerator:

2^4/2^14


however the book has:

[2^18 - 2^14]/2^14 = 2^4 - 1 = 16 - 1 = 15

which is reducing the fraction while subtracting the numerator? should you divide from both at the same time?....

am I doing the order of operations wrong?


thanks for any help! Maybe i've just been doing too many problems today....

 

[Ibracadabra]

Having a problem understanding this question in Math Destroyer....

its practice test 7, question 32

Evaluate:

[8^6 - 4^7]/2^14

this is as far as I got:

8^6 = 2^3x6 = 2^18

4^7 = 2^2x7 = 2^14

so....

[2^18 - 2^14]/2^14

My logic would be to subtract the two exponents in the numerator:

2^4/2^14


however the book has:

[2^18 - 2^14]/2^14 = 2^4 - 1 = 16 - 1 = 15

which is reducing the fraction while subtracting the numerator? should you divide from both at the same time?....

am I doing the order of operations wrong?


thanks for any help! Maybe i've just been doing too many problems today....

You are on the right tract, however, think of it this way.
3^3-3^2 is not equal to 3^1.
What they are doing in the equation is they are pulling out the common factor out, which is 2^14. That's why you end up getting 2^14(2^4-1)/2^14 and then you can cancel out 2^14, which gives you 2^4-1=15. 🙂

 

[UCB05]

subtracting powers of exponents is not a feasible operation. What's 2^5-2^2? 32-4=28 is certainly not 2^3.

What the question is doing is factoring out 2^14 in both terms of the numerator to cancel out the denominator.
[2^18 - 2^14]/2^14=
(2^14)(2^4-1)/(2^14)=
2^4-1=
15

which is reducing the fraction while subtracting the numerator?

That's exactly what they're doing using two properties:
(x-y)/z = x/z - y/z
and
(x^y)/(x^z) = x^(y-z)

 

[snaggletoof]

yeah, i actually ended up doing it like this....

[2^18/2^14] - [2^14/2^14]

I just needed to break up the two terms....now it makes

2^4 - 1


ahh.....I gotta take a break!



thanks !

 

[kanudo]

Whenever you see addition or subtraction with exponent you can not add or multiply the exponent. You can only add the base if the exponents are same.
For example ( x^2+x^2=2x^2) and ( x^2-x^2=0), and if the exponents are not the same then: ( 2^2+2^3=12).
So in your problem the exponents are not the same :

[(2^18/2^14) - (2^14/2^14)] = 2^4 - 1 = 16 - 1 = 15
hope it helps.

 

[mprs]

Some general "oh crap im stuck i don't know what to do" rules


1) you can convert to the same base
2) if multiplied or divided by eachother, use exponent rules
3) if added or subtracted, factor.

Pretty much what every1 else said 🙂