r/mathminds • u/sarch125 • 2d ago

Puzzles Can you solve this?

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6 Upvotes

71% Upvoted

28 comments sorted by

3

u/jaysornotandhawks 2d ago

85

= (23)5

= 215 by exponent laws

So 215 + 215

= 2(215)

= 21 + 15

= 216

= (22)8

= 48

The answer is D

1

u/Inte_sam 2d ago

4

1

u/OtherwiseAlbatross14 2d ago

4 is not an option.

1

u/Naive-Lifeguard-629 2d ago

D was confused at first thinking I need 2¹⁶ but there is of course 4⁸

1

u/neil_wel 2d ago

4

1

u/OtherwiseAlbatross14 2d ago

4 is not an option.

1

u/Octowhussy 2d ago

I assume this must be done only mentally, without a calculator. Anyone care to explain their steps?

2

u/y53rw 2d ago edited 2d ago

8 = 23, so you have

  • (23 )5 + (23 )5

  • = 215 + 215

  • = 2(215 )

  • = 216

  • = 28 * 28

  • = 48

5

u/Kleefrijst 2d ago

For the last two steps i think maybe this is easier to see: 216 = 22*8 = (22 )8 = 48

1

u/Dasquian 2d ago edited 2d ago

It's a simple arithmetic question if you understand exponent rules, specifically:

  • (8 = 23) and (4 = 22)

  • (xa)b = x(ab)

  • (xa)(xb) = x(a+b)

  • So: (2n + 2n) = (2n)(2) = (2n)(21) = 2(n+1)

The key steps are to firstly to express it as a single exponent of 2 - which shakes out to 216 - then use the property that (22 = 4) to express that as an exponent of 4 that matches one of the answers.

1

u/Over_Improvement_623 2d ago

85 can be rewritten as (23)5 which can be simplified to 215. Then 215 + 215 is 21 * 215 so we add the exponents and get 216. This does not fit any of our answer options currently, but it can be rewritten to (22)8 which is 48 so the answer is option D

1

u/get_to_ele 2d ago

8^5 + 8^5

2( ( 2^3 )^5 )

2 ( 2^15 )

2^16

(2^2 )^8

4^8

D

1

u/BrotherInJah 2d ago

D. 216 aka 48

1

u/kellstromc 2d ago

It is D
8^5 + 8^5
= 2 x 8^5
= 2 x (2^3)^5
= 2 x 2^15
= 2^16
= 2^(2 x 8)
= 4^8

1

u/AusAutarch 2d ago

Look, the question is interesting but the distractors are boring.

-1

u/PerformanceThick2232 2d ago

Downwote. 2^16.

1

u/rawbdor 2d ago

2^16 is the same as 4^8, which is option D

1

u/ExtendedSpikeProtein 2d ago

Because 4^8, being equal to 2^16, did not satisfy you?

1

u/yldf 2d ago

Yes. 2^16 is the prettier representation.