9x^-4-35x^-2=0

To solve the given equation 9x^(-4) - 35x^(-2) = 0, we can start by multiplying the entire equation by the common denominator x^(-4)x^(-2) to eliminate the denominators.

The equation becomes: 9 - 35x^(-2+(-4)) = 0
Simplifying, we have: 9 - 35x^(-6) = 0

We can now solve for x.

Step 1: Add 35x^(-6) to both sides of the equation to isolate the constant term:
9 - 35x^(-6) + 35x^(-6) = 0 + 35x^(-6)

Simplifying, we get: 9 = 35x^(-6)

Step 2: Divide both sides of the equation by 35 to isolate x^(-6):
9/35 = (35x^(-6))/35

Simplifying further, we get: 9/35 = x^(-6)

Step 3: To remove the negative exponent, we can take the reciprocal of both sides of the equation:
(35/9)^(-1/6) = (x^(-6))^(-1/6)

Simplifying, we get: (35/9)^(-1/6) = x

Step 4: Calculate the value of (35/9)^(-1/6) using a calculator or simplified fraction computation. This will give you the approximate value of x.

So, the solution to the equation 9x^(-4) - 35x^(-2) = 0 is x ≈ (35/9)^(-1/6).