Simplify. Write your answers without exponents. 16^-(3)/(4)= ((1)/(4))^-(5)/(2)= square

To simplify the given expressions, we can use the properties of exponents.<br /><br />1. $16^{-\frac {3}{4}}$<br /><br />We can rewrite $16$ as $2^4$ and then apply the power rule for exponents:<br /><br />$16^{-\frac {3}{4}} = (2^4)^{-\frac {3}{4}} = 2^{4 \cdot -\frac {3}{4}} = 2^{-3} = \frac {1}{2^3} = \frac {1}{8}$<br /><br />So, $16^{-\frac {3}{4}} = \frac {1}{8}$.<br /><br />2. $(\frac {1}{4})^{-\frac {5}{2}}$<br /><br />We can rewrite $\frac {1}{4}$ as $4^{-1}$ and then apply the power rule for exponents:<br /><br />$(\frac {1}{4})^{-\frac {5}{2}} = (4^{-1})^{-\frac {5}{2}} = 4^{-1 \cdot -\frac {5}{2}} = 4^{\frac {5}{2}} = (2^2)^{\frac {5}{2}} = 2^{2 \cdot \frac {5}{2}} = 2^5 = 32$<br /><br />So, $(\frac {1}{4})^{-\frac {5}{2}} = 32$.<br /><br />Therefore, the simplified expressions are:<br /><br />$16^{-\frac {3}{4}} = \frac {1}{8}$<br /><br />$(\frac {1}{4})^{-\frac {5}{2}} = 32$