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.