(n-27)^3/2=64

2 min read Jun 16, 2024

Solving the Equation: (n-27)^(3/2) = 64

This equation involves a fractional exponent, which can be a bit tricky at first. Let's break it down step-by-step to find the solution for 'n'.

1. Isolate the Term with the Exponent

The first step is to isolate the term with the fractional exponent: (n-27)^(3/2). We can do this by raising both sides of the equation to the power of (2/3).

(n-27)^(3/2 * 2/3) = 64^(2/3)

This simplifies to:

(n-27) = 64^(2/3)

2. Simplify the Right Side

Now, we need to simplify the right side of the equation. Remember that a fractional exponent means taking a root and then raising it to a power. In this case, 64^(2/3) means taking the cube root of 64 and then squaring the result:

64^(2/3) = (³√64)² = 4² = 16

3. Solve for 'n'

Now we have:

(n-27) = 16

To solve for 'n', simply add 27 to both sides of the equation:

n = 16 + 27

n = 43

Conclusion

Therefore, the solution to the equation (n-27)^(3/2) = 64 is n = 43.