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(x-2/9)^3=(2/3)^6

less than a minute read Jun 17, 2024
(x-2/9)^3=(2/3)^6

Solving the Equation (x-2/9)^3 = (2/3)^6

This equation involves exponents and requires a bit of algebraic manipulation to solve for 'x'. Here's how to break it down:

1. Simplify the right side:

  • (2/3)^6 = (2/3) * (2/3) * (2/3) * (2/3) * (2/3) * (2/3) = 64/729

2. Take the cube root of both sides:

  • The cube root of (x-2/9)^3 is simply (x-2/9)
  • The cube root of 64/729 is 4/9 (since 444 = 64 and 999 = 729)

3. Solve for 'x':

  • Now we have: x - 2/9 = 4/9
  • Add 2/9 to both sides: x = 4/9 + 2/9
  • Therefore, x = 6/9

4. Simplify:

  • x = 2/3

Solution: The solution to the equation (x-2/9)^3 = (2/3)^6 is x = 2/3.

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