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CHAPTER 11 REVIEW EXERCISES

CONCEPT CHECK EXERCISES

Determine each of the following as being either true or false. If it is false, explain why.

$2 x^{0} = 1$
$\sqrt{16 + 4} = 6$
$(16^{- 1/2}) (\frac{1}{4^{- 2}}) = 2$
$\sqrt{48} - \sqrt{27} = \sqrt{3}$
$\frac{1}{\sqrt{3} - \sqrt{2}} = \sqrt{3} + \sqrt{2}$
$\sqrt{5} \sqrt{7} = \sqrt{35}$

PRACTICE AND APPLICATIONS

In Exercises 7–34, express each expression in simplest form with only positive exponents.

$8 x^{- 3} y^{0}$
${(2 c)}^{- 1} z^{- 2}$
$\frac{9 c^{- 1}}{d^{- 3}}$
$\frac{- 5 x^{0}}{3 y^{- 1}}$
$3 {(25)}^{3/2}$
$32^{2/5}$
$8 (400^{- 3/2})$
$7 {(1000)}^{- 2/3}$
${(\frac{3}{t^{2}})}^{- 2}$
${(\frac{2 x^{3}}{3})}^{- 3}$
$\frac{- 8^{2/3}}{49^{- 1/2}}$
$\frac{4^{- 45}}{2^{- 90}}$
${(2 a^{2/3} b^{1/6})}^{6}$
${(a x^{- 1/2} y^{1/4})}^{8}$
${(- 32 m^{15} n^{10})}^{3/5}$
${(27 x^{- 6} y^{9})}^{2/3}$
$6 L^{- 2} - 4 C^{- 1}$
$C^{4} C^{- 1} + {(C^{4})}^{- 1}$
$\frac{3 x^{- 1}}{3 x^{- 1} + y^{- 1}}$
$\frac{9 a}{{(2 a)}^{- 1} - a}$
${(a - 3 b^{- 1})}^{- 1}$
${(2 s^{- 2} + t)}^{- 2}$
${(x^{3} - y^{- 3})}^{1/3}$
${(27 a^{3})}^{2/3} {(a^{- 2} + 1)}^{1/2}$
${(W^{2} - 2 W H + H^{2})}^{- 1/2}$
${[\frac{{(9 a)}^{0} {(4 x^{2})}^{1/3} (3 b^{1/2})}{{(2 b^{0})}^{2}}]}^{- 6}$
$2 x (x$

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