Question

HELP
8 Prove that 8^6+4^11 is divisible by 17. Answer __*17

Answer 1

Answer:

262,144 goes in the blank

Step-by-step explanation:

8^6 = 262,144

4^11 = 4,194,304

4,194,304 + 262,144 = 4,456,448

4,456,448 ÷ 17 = 262,144

Answer 2

You can use the fact that 8 is cube of 3 and 4 is square of 2.

The value in the blank space given is $2^{18}$

Given that:

• To prove that $8^6+4^{11}$ is divisible by 17

Converting  $8^6+4^{11}$  in terms of 2:

$8^6 = (2^3)^6 = 2^{3 \times 6} = 2^{18}$

$4^{11} = (2^2)^{11} = 2^{2 \times 11} = 2^{22}$

Thus,

$8^6 + 4^{11} = 2^{18} + 2^{22} = 2^{18}(1 + 2^{4}}) = 2^{18} \times 17$

Thus, it is multiple of 17 and thus, divisible by 17.

The value in the blank space given is $2^{18}$

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