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
. We can multiply nominator and denominator by the any number (but the same) and get another numbers but ratio will be the same, so equivalent.