Section 1
Review of the Rules of Exponents
State which exponent rule must be used to simplify each exercise. Then simplify.$\frac{k^{10}}{k^{4}}$
State which exponent rule must be used to simplify each exercise. Then simplify.$p^{5} \cdot p^{2}$
State which exponent rule must be used to simplify each exercise. Then simplify.$(2 h)^{4}$
State which exponent rule must be used to simplify each exercise. Then simplify.$\left(\frac{5}{w}\right)^{3}$
Evaluate using the rules of exponents.$2^{2} \cdot 2^{4}$
Evaluate using the rules of exponents.$(-3)^{2} \cdot(-3)$
Evaluate using the rules of exponents.$\frac{(-4)^{8}}{(-4)^{5}}$
Evaluate using the rules of exponents.$\frac{2^{10}}{2^{6}}$
Evaluate using the rules of exponents.$6^{-1}$
Evaluate using the rules of exponents.$(12)^{-2}$
Evaluate using the rules of exponents.$\left(\frac{1}{9}\right)^{-2}$
Evaluate using the rules of exponents.$\left(-\frac{1}{5}\right)^{-3}$
Evaluate using the rules of exponents.$\left(\frac{3}{2}\right)^{-4}$
Evaluate using the rules of exponents.$\left(\frac{7}{9}\right)^{-2}$
Evaluate using the rules of exponents.$6^{0}+\left(-\frac{1}{2}\right)^{-5}$
Evaluate using the rules of exponents.$\left(\frac{1}{4}\right)^{-2}+\left(\frac{1}{4}\right)^{0}$
Evaluate using the rules of exponents.$\frac{8^{5}}{8^{7}}$
Evaluate using the rules of exponents.$\frac{2^{7}}{2^{12}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$t^{5} \cdot t^{8}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$n^{10} \cdot n^{6}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(-8 c^{4}\right)\left(2 c^{5}\right)$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(3 w^{9}\right)(-7 w)$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(z^{6}\right)^{4}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(y^{3}\right)^{2}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(5 p^{10}\right)^{3}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(-6 m^{4}\right)^{2}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(-\frac{2}{3} a^{7} b\right)^{3}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(\frac{7}{10} r^{2} s^{5}\right)^{2}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{f^{11}}{f^{7}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{u^{9}}{u^{8}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{36 k^{8}}{12 k^{5}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{9 d^{10}}{54 d^{6}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{7 m^{4}}{56 m^{2}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{x^{3}}{x^{9}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{v^{2}}{v^{5}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{m^{2}}{m^{3}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{t^{3}}{t^{3}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{45 k^{-2}}{30 k^{2}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{22 n^{-9}}{55 n^{-3}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$5\left(2 m^{4} n^{7}\right)^{2}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$2\left(-3 a^{8} b\right)^{3}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(6 y^{2}\right)\left(2 y^{3}\right)^{2}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(-c^{4}\right)\left(5 c^{9}\right)^{3}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(\frac{7 a^{4}}{b^{-1}}\right)^{-2}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(\frac{3 t^{-3}}{2 u}\right)^{-4}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{a^{-12} b^{7}}{a^{-9} b^{2}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{m n^{-4}}{m^{9} n^{7}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{\left(x^{2} y^{-3}\right)^{4}}{x^{5} y^{8}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{10 r^{-6} t}{\left(4 r^{-5} t^{4}\right)^{3}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{12 a^{6} b c^{-9}}{\left(3 a^{2} b^{-7} c^{4}\right)^{2}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{\left(-7 k^{2} m^{-3} n^{-1}\right)^{2}}{14 k m^{-2} n^{2}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(x y^{-3}\right)^{-5}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$-\left(s^{-6} t^{2}\right)^{-4}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(\frac{a^{2} b}{4 c^{2}}\right)^{-3}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(\frac{2 s^{3}}{r t^{4}}\right)^{-5}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(\frac{7 h^{-1} k^{9}}{21 h^{-5} k^{5}}\right)^{-2}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(\frac{24 m^{8} n^{-3}}{16 m n}\right)^{-3}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(\frac{15 c d^{-4}}{5 c^{3} d^{-10}}\right)^{-3}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\left(\frac{10 x^{-5} y}{20 x^{5} y^{-3}}\right)^{-2}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{\left(2 u^{-5} v^{2} w^{4}\right)^{-5}}{\left(u^{6} v^{-7} w^{-10}\right)^{2}}$
Simplify. Assume all variables represent nonzero real numbers. The answer should not contain negative exponents.$\frac{\left(a^{-10} b^{-5} c^{2}\right)^{4}}{6\left(a^{9} b c^{-4}\right)^{-2}}$
Write expressions for the area and perimeter for each rectangle.
Simplify. Assume that the variables represent nonzero integers.$k^{4 a} \cdot k^{2 a}$
Simplify. Assume that the variables represent nonzero integers.$r^{9 y} \cdot r^{y}$
Simplify. Assume that the variables represent nonzero integers.$\left(g^{2 x}\right)^{4}$
Simplify. Assume that the variables represent nonzero integers.$\left(t^{5 c}\right)^{3}$
Simplify. Assume that the variables represent nonzero integers.$\frac{x^{7 b}}{x^{4 b}}$
Simplify. Assume that the variables represent nonzero integers.$\frac{m^{10 u}}{m^{3 u}}$
Simplify. Assume that the variables represent nonzero integers.$\left(2 r^{6 m}\right)^{-3}$
Simplify. Assume that the variables represent nonzero integers.$\left(5 a^{-2 x}\right)^{-2}$