(2/9×7/8÷7/18) ^3

To simplify the expression \((\frac{2}{9} \times \frac{7}{8} \div \frac{7}{18})^3\), we will follow these steps:

1. Multiply and divide the fractions:

   Division of fractions can be converted to multiplication by taking the reciprocal of the divisor. So, \[ \frac{7}{8} \div \frac{7}{18} = \frac{7}{8} \times \frac{18}{7} \]

   The \(7\) in the numerator and denominator cancel each other out: \[ \frac{18}{8} = \frac{9}{4} \quad \text{(by dividing both numerator and denominator by 2)} \]

2. Now, substitute this back into the expression:

   \[ \frac{2}{9} \times \frac{9}{4} \]

   Now, multiplying the fractions: \[ = \frac{2 \times 9}{9 \times 4} \] The \(9\) in the numerator and denominator also cancels each other out: \[ = \frac{2}{4} = \frac{1}{2} \quad \text{(by dividing both numerator and denominator by 2)} \]

3. Now, take the cube of \(\frac{1}{2}\):

   \[ \left(\frac{1}{2}\right)^3 = \frac{1^3}{2^3} = \frac{1}{8} \]

So, the simplified expression is: \[ \boxed{\frac{1}{8}} \]