%5E2%2F3%3D16.jpeg "(x-5)^2/3=16")
Solving the Equation: (x - 5)^(2/3) = 16
This equation involves a fractional exponent, which can be a bit tricky to work with. Here's how to solve it step by step:
1. Isolate the term with the fractional exponent:
The term with the fractional exponent is already isolated on the left side of the equation.
2. Raise both sides to the reciprocal of the fractional exponent:
The reciprocal of 2/3 is 3/2. Raising both sides to this power will eliminate the fractional exponent:
[(x - 5)^(2/3)]^(3/2) = 16^(3/2)
3. Simplify:
On the left side, the exponents multiply: (2/3) * (3/2) = 1, leaving us with (x - 5). On the right side, 16^(3/2) = (16^(1/2))^3 = 4^3 = 64
This gives us: x - 5 = 64
4. Solve for x:
Add 5 to both sides of the equation: x = 64 + 5
5. The solution:
Therefore, the solution to the equation (x - 5)^(2/3) = 16 is x = 69.