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3 years ago

Prove the divisbility of the following numbers.

Mathematics

1 answer:

Anastaziya [24]3 years ago

7 0

Answer:

3^16

Step-by-step explanation:

12^8 * 9^12

Rewrite 12 as 3*4 and 9 as 3*3

(3*4)^8 * (3*3)^12

We know that (ab)^c = a^c * b^c

3^8 4^8 3^12 3^12

We can write 4 as 2^2

3^8 2^2^8 3^12 3^12

We know a^b^c = a^(b*c)

3^8 2^(2*8) 3^12 3^12

3^8 2^(16) 3^12 3^12

We also know that a^b *a^c *a^d = a^(b+c+d)

2^(16) 3^8 3^12 3^12

2^(16) 3^(8+12+12)

2^16 3^(32)

But we need 6 ^16 so we will need a 3^16 3^32 = 3^16 * ^16 (16+16=32)

2^16 *3^16 *3^16

Remember a^b*c^b = (ac)^b

(2*3)^16 3^16

6^16 3^16

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