express the following as a rational number with positive exponent:
[2/9]^-2/[2/9]^-3*[2/9]^-4

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Solution

$\frac{{(\frac{2}{9})}^{- 2}}{{(\frac{2}{9})}^{- 3} \times {(\frac{2}{9})}^{- 4}} = \frac{{(\frac{2}{9})}^{- 2}}{{(\frac{2}{9})}^{- 3 - 4}} [Using, x^{a} \times x^{b} = x^{a + b}] = \frac{{(\frac{2}{9})}^{- 2}}{{(\frac{2}{9})}^{- 7}} = {(\frac{2}{9})}^{- 2 + 7} [Using, \frac{x^{a}}{x^{b}} = x^{a - b}] = {(\frac{2}{9})}^{5} = \frac{32}{59049} Hence, \frac{{(\frac{2}{9})}^{- 2}}{{(\frac{2}{9})}^{- 3} \times {(\frac{2}{9})}^{- 4}} = \frac{32}{59049}$

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