Solving x^(2/3) = 1 Made Easy: Step-by-Step Tutorial

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Solving the Equation: x^(2/3) = 1

Exponential equations can seem tricky at first, but once you understand the rules of exponents, they become much easier to solve. In this post, we’ll explore how to solve the equation x^(2/3) = 1 and uncover the logic behind it.

 

Understanding the Equation

The equation x^(2/3) = 1involves a fractional exponent. Here, the exponent 2/3 means we first square x and then take the cube root of that result. Our goal is to find the value of x that satisfies this equation.

 

Step 1: Eliminate the Fractional Exponent

To solve for x, we need to eliminate the fractional exponent. We can do this by raising both sides of the equation to the reciprocal of 2/3, which is 3/2. This will cancel out the exponent on the left side:

{x^(2/3)}^(3/2) = 1

When we multiply the exponents on the left side, we get:

X^1 = 1^(2/3)

And on the right side:

1^(2/3) = 1

This simplifies the equation to:

X=1

 

Step 2: Check the Solution

It's always a good practice to check your solution by substituting it back into the original equation. Plugging x =1 into the original equation x ^(2/3) = 1

Since this is a true statement, we confirm that x = 1 is indeed the correct solution.

Conclusion

The equation x^(2/3) = 1 might seem daunting at first, but by understanding how to work with fractional exponents, solving it becomes straightforward. Remember, the key is to eliminate the fractional exponent by raising both sides to the appropriate power. With practice, these kinds of problems will become second nature to you!

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