2 to the 12th power = 4,096. How many other whole numbers can you raise to a power to get 4,096! Explain or show your reasoning.

Mathematics

1 answer:

Sonja [21]2 years ago

7 0

Answer:

Other whole numbers that can be raised to a power to get 4,096 are 4, 8, 16 and 64

Step-by-step explanation:

Given;

2¹² = 4096

Other whole numbers that can be raised to a power to get 4,096 are obtained as follows;

$if \ (a^x)^y = a^{xy}\\\\ (2^2)^6 = 4,096\\\\(4)^6 = 4,096\\\\Thus, \ the \ first \ whole \ number \ is \ 4\\\\(2^3)^4 = 4,096\\\\(8)^4 = 4,096\\\\Thus, \ the \ second \ whole \ number \ is \ 8\\\\(2^4)^3 = 4,096\\\\(16)^3 = 4,096\\\\Thus, \ the \ third \ whole \ number \ is \ 16\\\\(2^6)^2 = 4,096\\\\(64)^2 = 4,096\\\\Thus, \ the \ fourth \ whole \ number \ is \ 64$

Therefore, Other whole numbers that can be raised to a power to get 4,096 are 4, 8, 16 and 64

You might be interested in

Mari has 39 square feet of patio bricks. Each square brick has sides 1 foot long. What is the greatest perimeter of a rectangle

Margaret [11]

I think you would do 39 x 4 because if the SQUARE brick has sides 1 foot long, you count up the sides and get 4 feet. She has 29 square feet of patio bricks so you would multiply 39 x 4. I don't know if this is correct. Hopefully I helped!

3 0

2 years ago

determine whether the lines intersect and if so find the point of intersection and the cosine of the angle of intersection x=4t+

Fittoniya [83]

Answer:

As the lines are not intersecting nor parallel, they must be skew.

Step-by-step explanation:

Question is incomplete, we consider the nearest match available online.

Parametric equations of two lines are:

L₁ : x=4t+2 , y = 3 , z =-t+1

L₂: x=2s+2 , y= 2s+5 , z = s+1

If lines are parallel then parametric coordinates must be equal scalar multiple of each other which s not true here.

$4t+2=2s+2 ---(1)\\ \\3=2s+5---(2) \\\\-t+1=s+1---(3)$

If lines are intersecting then parametric coordinates must be equal for some value of t and s.

$From (3)\\-t=s\\From (2)\\\\s=\frac{3-5}{2}\\\\s=-1\\\implies t=1\\\\To\,\,check\,\, the \,\,values \,\,of \,\,s\,\, and \,\,t \,\,for\,\,intersection\,\,put \,\,them\,\, in\,\, (1)\\\\4(1)+2= 2(-1)+2\\ 6\ne0$