1.4.1.1: 1.4.1 and 1.4.2 Exercises
- Page ID
- 83069
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Section 1.4.1 and 1.4.2 Exercises
- Rewrite each expression using exponents.
- \( 3 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \)
- \( (2.45)(2.45)(2.45)(2.45)(2.45)\)
- Rewrite these expressions with positive exponents only. Then evaluate the expression.
- \(5^{-2} \)
- \( \dfrac{1}{5^{-2}} \)
- \( \dfrac{3 \cdot 5}{5^{-2}}\)
- Evaluate:
- 47\(^0\)+ 5
- \( (5.2+5.97)^{0} \)
- \( -3(5^{1}-4\cdot 2^{0})\)
- Write these numbers in order by size: \(-5^2, 5^{-2}, (5)^2, -5^{-2} \)
- Evaluate:
- \( 3^6 \cdot 3^{-3}\)
- \( \dfrac{4^{-2}}{4^{-3}} \)
- Evaluate. Write the results as a fraction and as a decimal.
- 10\(^{-5}\)
- 5\(^{-2}\)
- (-2)\(^{-3}\)
- 6\(\times 10^{-2}\)
- \(\dfrac{16}{[(4\times 10^{-2}) - (2 \times 10^{-2})]}\)
- Are any of these the same: 4\(^{-2}\) , (-4)\(^{-2}\) , -4\(^2\) ,(-4)\(^2\) ,(1/4)\(^{-2}\) , (-1/4)\(^2\)
- Evaluate for \(x=2, y=3,\) and \(z=5\).
- \( (4x^{2}y^{3})\cdot (3x^{-3}y^{-2}) \)
- \( \dfrac{24x^{-2}y^{3}}{6x^{3}y^{-1}}\)
- \( \left(\dfrac{2x^{-2}y^{-3}}{z^{2}} \right) \)
- Complete the following:
- Show why \((2^3)^2=2^{3\cdot 2} \).
- Show why \((2\cdot 3)^2=2^{2}\cdot 3^{2} \).
- Show why\( \left(\dfrac{2}{3} \right)^{2}=\dfrac{2^2}{3^2} \)