Question

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

Answer 1

Answer:

c) $6^6$

Step-by-step explanation:

$\dfrac{12^6}{2^6}$

factor  $12^6 =(3 \cdot 4)^6= (3 \cdot 2^2)^6=3^6 \cdot 2^{12}$

$\implies \dfrac{12^6}{2^6}=\dfrac{3^6 \cdot 2^{12}}{2^6}$

Apply exponent rule $\frac{a^b}{a^c} =a^{b-c}$:

$\implies \dfrac{3^6 \cdot 2^{12}}{2^6}=3^6 \cdot 2^6$

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

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

Answer 2

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:)