Question

Which expression is equivalent to 12^6 / 2^6
a. 6^0
b. 1/6^6
c. 6^6
d. 6

Answer 1

Hey there!

12^6 / 2^6

12^6

= 12 * 12 * 12 * 12 * 12 * 12

= 144 * 144 * 144

= 20,736 * 144

= 2,985,984

= 2,985,984/2^6

2^6

= 2 * 2 * 2 * 2 * 2 * 2

= 4 * 4 * 4

= 16 * 4

= 64

= 2,985,984/64
= 2,985,984 ÷ 64 / 64 ÷ 64

= 46,656 / 1

= 46,656 ÷ 1

= 46,656

LOOKING FOR SOMETHING THATS EQUIVALENT TO: 46,656

PROCESS OF ELIMINATION

6^0

= 6 * 1

= 6

it’s NOT

1/6^6

= 1 / 6 * 6 * 6 * 6 * 6 * 6

= 1 / 36 * 36 * 36

= 1 / 1,296 * 36

= 1 / 46,656

It’s NOT option B

6^6

= 6 * 6 * 6 * 6 * 6 * 6

= 36 * 36 * 36

= 1,296 * 36

= 46,656

Option C IS possibly your answer

6

= 6
Its NOT option D

Therefore, your answer is:

Option C. 6^6

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer 2

c)
`6^6`

Explanation:

`(12^6)/(2^6)`

factor
`12^6 =(3 \cdot 4)^6= (3 \cdot 2^2)^6=3^6 \cdot 2^(12)`

`\implies (12^6)/(2^6)=(3^6 \cdot 2^(12))/(2^6)`

Apply exponent rule
`(a^b)/(a^c) =a^(b-c)`:

`\implies (3^6 \cdot 2^(12))/(2^6)=3^6 \cdot 2^6`

Apply exponent rule
`(a^b \cdot c^b)=(ac)^b`:

`\implies 3^6 \cdot 2^6=(3 \cdot 2)^6=6^6`