If q^1/2 = x, x^-1/4 = 4^-1/2, what is the value of q? Plz help me!
x ^ - 1/4 = 4 ^ -1/2
mean:
1 / fourth root of x = 1 / square root of 4
1 / fourth root of x = 1 / 2
Taking reciprocial of both sides:
fourth root of x = 2
Rise both sides to the power of four
x = 2 ^ 4
x = 16
q^ 1/2 = x mean :
square root of q = x
Rise both sides to the power of two
q = x ^ 2
q = 16 ^ 2
q = 256
x^-1/4 = 4^-1/2, what is the value of q?^
raise both sides to the - 4th power
multiply - 1/4 times -4 = 1
multiply -1/2 times -4 = 2
x = 4^2 x = 16 Now you can find q.
To find the value of q, let's simplify the given equations step by step.
1. We are given that q^(1/2) = x.
Since x is equal to q^(1/2), we can write the equation as:
x = q^(1/2)
2. We are also given that x^(-1/4) = 4^(-1/2).
Let's simplify the right side first:
4^(-1/2) means the reciprocal (inverse) of the square root of 4.
The square root of 4 is 2, so:
4^(-1/2) = (1/2)^(-1) = 1/(1/2) = 2.
So, the equation becomes:
x^(-1/4) = 2.
3. Now, substitute the value of x from the first equation into the second equation:
(q^(1/2))^(-1/4) = 2.
To simplify the left side, we need to multiply the exponents:
q^((1/2)*(-1/4)) = 2.
1/2 * -1/4 = -1/8.
Simplifying further:
q^(-1/8) = 2.
4. To solve for q, raise both sides of the equation to the power of -8:
(q^(-1/8))^(-8) = 2^(-8).
Simplifying the left side:
q = 2^(-8).
5. Calculate 2^(-8):
2^(-8) = 1/(2^8) = 1/256.
Therefore, the value of q is 1/256.
So, q = 1/256.