Simplify the expression below. \( \frac{2}{11} x^{7}-\frac{9}{10} x^{7} \)

To simplify the expression \( \frac{2}{11} x^{7}-\frac{9}{10} x^{7} \), first, notice that both terms have a common factor of \( x^{7} \). Factor out \( x^{7} \): \[ x^{7} \left( \frac{2}{11} - \frac{9}{10} \right) \] Now, we need a common denominator to combine the fractions within the parentheses. The least common multiple of 11 and 10 is 110. Rewrite each fraction: \[ \frac{2}{11} = \frac{2 \times 10}{11 \times 10} = \frac{20}{110} \] \[ \frac{9}{10} = \frac{9 \times 11}{10 \times 11} = \frac{99}{110} \] Now, substitute these back into the expression: \[ x^{7} \left( \frac{20}{110} - \frac{99}{110} \right) = x^{7} \left( \frac{20 - 99}{110} \right) = x^{7} \left( \frac{-79}{110} \right) \] Thus, the simplified expression is: \[ -\frac{79}{110} x^{7} \]