Question

Are You Ready for More?: Two raised to the 12th power is equal to 4,096. How many other

whole numbers can you raise to a power and get 4,096? Explain or show your reasoning.

(1 Point)

2^12 = 4096

Answer 1

4, 8, 16,64 and 4096.

Explanation:

We are already given:
`4096=2^(12)`

To determine other whole numbers that can be raised to a power to obtain 4096, we apply the product rule of indices.

Product Rule of Indices:
`a^(xy)=(a^x)^y`

Now 12 can be factored in the following ways where one of the terms must be a perfect square:

• 12=2 X 6
• 12 =6 X 2
• 12 =3 X 4
• 12 =4 X 3
• 12=1 X 12

`2^(12)=(2^2)^6=4^6\\\\2^(12)=(2^6)^2=64^2\\\\2^(12)=(2^4)^3=16^3\\\\2^(12)=(2^3)^4=(8^2)^2=8^(2*2)=8^4\\\\2^(12)=(2^(12))^1=4096^1 $(This is the trivial case)`

Therefore, the other whole numbers that can be raised tp a power to obtain 4096 are: 4, 8, 16, 64 and 4096.