Question

Just need the answers for these 3 questions please, and how to do them (:

Answer 1

Answer:

a) 7

b)64

c)2

Step-by-step explanation:

look at images

Answer 2

Answer:

x = 2

Step-by-step explanation:

The topic here is "fractional exponents."

Review:  2^3 = 8 (this is the cube of 2), and so the inverse function is

            8^(1/3) = 2    ("8 raised to the fractional exponent 1/3 is 2"

Question a)  49^(1/2) ("49 to the power 1/2") can be rewritten as

(7^2)^(1/2), which simplifies to 7^(2*1/2) = 7^1  =  7

Caution:  this is exponentiation, not division.  So 49^(1/2) does not equal 49/2.

Question b)     (     )^(1/3)  =  4

I would prefer to write this as x^(1/3) = 4 and set the goal of finding the value of the base, x.

Then x^(1/3) = 4   ("x raised to the power 1/3 is 4")

Let's elimiinate the fractional exponent on the left by cubing both sides of the equation:

{x^(1/3)}^3 = 4^3, or, after simplification,

x^1 = 64, or, in simplest form,

x = 64

Question c)

Notice that the base here is 1/100

and that the square root of 1 is 1 and that of 100 is 10.

Therefore, the given

{1/100} is equivalent to {1/10)^2

and so we have:

          1                      1

  (------------)^(1/x) = -------   (we are to find x)

     10^2                    10

Note that 10 is the square root of 10^2, also the square root of 100.

So let's take the square root of 10^2.  We get 10.

Therefore, try x = 2 and see whether the given equation is true:

      1                      1

{---------)^(1/2)   =  ------

 100                     10

The square root of 1 is just 1.  The square root of 100 is 10.  

Therefore the above equation becomes

 1        1

----- = -----  and so  x = 2 is correct.

10      10