3) (a^-11 cdot a^4)/(a^-3)=a^-11 cdot a^4: a^-3

To simplify the expression \( \frac{a^{-11} \cdot a^{4}}{a^{-3}} \), we can use the properties of exponents.<br /><br />First, let's simplify the numerator:<br />\( a^{-11} \cdot a^{4} = a^{-11+4} = a^{-7} \)<br /><br />Now, we can rewrite the expression as:<br />\( \frac{a^{-7}}{a^{-3}} \)<br /><br />Using the property of exponents that states \({a^m}{a^n} = a^{m-n} \), we can simplify the expression further:<br />\( \frac{a^{-7}}{a^{-3}} = a^{-7-(-3)} = a^{-7+3} = a^{-4} \)<br /><br />Therefore, the simplified expression is \( a^{-4} \).