Question

Simplify and express with positive exponents $\left[{\left(\frac{9}{11}\right)}^{-3}\times {\left(\frac{9}{11}\right)}^{-7}\right]÷{\left(\frac{9}{11}\right)}^{-3}$

Answer 1

$[{\left(\frac{9}{11}\right)}^{-3}\times {\left(\frac{9}{11}\right)}^{-7}]÷{\left(\frac{9}{11}\right)}^{-3}$

$={\left(\frac{9}{11}\right)}^{-3+(-7)}÷{\left(\frac{9}{11}\right)}^{-3}$

$={\left(\frac{9}{11}\right)}^{-10}÷{\left(\frac{9}{11}\right)}^{-3}$

$={\left(\frac{9}{11}\right)}^{-10-(-3)}$

$={\left(\frac{9}{11}\right)}^{-7}$

$={\left(\frac{11}{9}\right)}^7$