9x9x9.jpeg "(1/3)9x9x9")
Understanding (1/3)⁹ x ⁹ x ⁹
This expression involves several mathematical operations, let's break it down step-by-step:
1. Exponent: (1/3)⁹
This part of the expression represents (1/3) multiplied by itself nine times.
Calculation: (1/3)⁹ = (1/3) * (1/3) * (1/3) * (1/3) * (1/3) * (1/3) * (1/3) * (1/3) * (1/3) = 1/19683
2. Multiplication: (1/19683) x ⁹ x ⁹
Now we have the result of the exponent and need to multiply it by 9 and then again by 9.
Calculation: (1/19683) x ⁹ x ⁹ = (9/19683) x ⁹ = 81/19683
Simplifying the Result
The fraction 81/19683 can be simplified by finding the greatest common factor (GCF) of the numerator and denominator. In this case, the GCF is 81.
Simplified Result: 81/19683 ÷ 81/81 = 1/243
Conclusion
Therefore, (1/3)⁹ x ⁹ x ⁹ simplifies to 1/243.