How do you solve an equation with a fraction like x^(2/3) +13=17. I don't think the quadratic formula would work for this method, and neither would completing the square. What should I do?
To solve this equation with a fractional exponent, you need to isolate the variable x. Since the exponent is 2/3, it means that we have a cube root involved.
Here's how you can solve it step by step:
Step 1: Subtract 13 from both sides of the equation:
x^(2/3) = 17 - 13
x^(2/3) = 4
Step 2: To eliminate the fractional exponent, raise both sides of the equation to the power that is the reciprocal of the exponent. In this case, the exponent is 2/3, so you will raise both sides to the power of 3/2:
(x^(2/3))^(3/2) = 4^(3/2)
Step 3: Simplify the left side of the equation by applying the exponent rules:
x^((2/3)*(3/2)) = 4^(3/2)
x^1 = 4^(3/2)
x = 4^(3/2)
Step 4: Evaluate the right side by simplifying the exponent:
x = sqrt(4^3)
x = sqrt(64)
x = ±8
Therefore, the solutions to the equation x^(2/3) + 13 = 17 are x = 8 and x = -8.