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Exponents

Evaluate negative exponents

Evaluate 2-4

$2^{-4}=\frac{1}{2^{4}}=\frac{1}{16}$

Evaluate 2-3

 $2^{-3}=\frac{1}{2^{3}}$ Definition of negative exponents $=\frac{1}{8}$ The cube of 2 is 8

Evalate (-3)-2

 $(-3)^{-2}=\frac{1}{(-3)^{2}}$ Definition of negative exponents $=\frac{1}{9}$ The square of -3 is 9

Evaluate $(\frac{1}{3})^{-1}$

$(\frac{1}{3})^{-1}=(\frac{3}{1})^{1}=\frac{3}{1}=3$

Evaluate $-(\frac{2}{3})^{-2}$

$-(\frac{2}{3})^{-2}=-(\frac{3}{2})^{2}=-\frac{3\cdot3}{2\cdot2}=-\frac{9}{4}$