1.4.1: Ejercicios 1.4
- Page ID
- 113941
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Términos y Conceptos
Ejercicio\(\PageIndex{1}\)
¿Se aplican las reglas de exponente a las funciones raíz? Explique.
- Contestar
-
Sí, una función raíz es solo una función de potencia con un exponente fraccionario.
Ejercicio\(\PageIndex{2}\)
Explique por qué un exponente negativo mueve el término al denominador y le da un exponente positivo.
- Contestar
-
Un exponente positivo significa que estamos multiplicando ese término repetidamente, un exponente negativo significa que estamos dividiendo por ese término repetidamente.
Ejercicio\(\PageIndex{3}\)
Es\(3x(2x+3)^{-5/3}\) in radical or exponential form?
- Contestar
-
Forma exponencial
Ejercicio\(\PageIndex{4}\)
Es\(\displaystyle \frac{3x}{\sqrt[3]{(2x+3)^5}}\) in radical or exponential form?
- Contestar
-
Forma radical
Problemas
En ejercicios\(\PageIndex{5}\) -\(\PageIndex{7}\), escribir el término dado sin utilizar exponentes.
Ejercicio\(\PageIndex{5}\)
\(\displaystyle (8x_1-5x_2+11)^{-1/3}\)
- Contestar
-
\(\displaystyle \frac{1}{\sqrt[3]{8x_1-5x_2+11}}\)
Ejercicio\(\PageIndex{6}\)
\(\displaystyle (-2x+y)^{-1/5}\)
- Contestar
-
\(\displaystyle \frac{1}{\sqrt[5]{-2x+y}}\)
Ejercicio\(\PageIndex{7}\)
\(\displaystyle (5x-2)^{1/4}\)
- Contestar
-
\(\displaystyle \sqrt[4]{5x-2}\)
En ejercicios\(\PageIndex{8}\) -\(\PageIndex{10}\), simplificar y escribir el término dado sin usar radicales.
Ejercicio\(\PageIndex{8}\)
\(\displaystyle \Bigg( \sqrt{x} + \frac{1}{\sqrt{x}} \Bigg)^2\)
- Contestar
-
\(\displaystyle x + 2 + \frac{1}{x}\)
Ejercicio\(\PageIndex{9}\)
\(\displaystyle (\sqrt{x})^2 + \Bigg(\frac{1}{\sqrt{x}} \Bigg)^2\)
- Contestar
-
\(\displaystyle x + \frac{1}{x}\)
Ejercicio\(\PageIndex{10}\)
\(\displaystyle \Bigg(\sqrt[3]{x} +1 \Bigg)^3\)
- Contestar
-
\(\displaystyle x + 3x^{2/3} + 3x^{1/3} + 1\)
En ejercicios\(\PageIndex{11}\) -\(\PageIndex{17}\), simplifica el término dado y escribe tu respuesta sin exponentes negativos.
Ejercicio\(\PageIndex{11}\)
\(\displaystyle \Bigg( \frac{-5x^{-1/4}y^3}{x^{1/4}y^{1/2}}\Bigg)^2\)
- Contestar
-
\(\displaystyle \frac{25y^5}{x}, y \neq 0\)
Ejercicio\(\PageIndex{12}\)
\(\displaystyle \Bigg( \frac{-2x^{2/3}y^2}{x^{-2}y^{1/2}}\Bigg)^6\)
- Contestar
-
\(\displaystyle 64x^{16}y^9; x,y \neq 0\)
Ejercicio\(\PageIndex{13}\)
\(\displaystyle \Bigg( \frac{-3s^{2/3}t^2}{4s^3t^{5/3}}\Bigg)^3\)
- Contestar
-
\(\displaystyle \frac{-27t}{64s^7}, t\neq 0\)
Ejercicio\(\PageIndex{14}\)
\(\displaystyle -3(x^2+4x+4)^{-4}(2x+4)\)
- Contestar
-
\(\displaystyle \frac{-6}{(x+2)^7}\)
Ejercicio\(\PageIndex{15}\)
\(\displaystyle \frac{1}{3}(x^4)^{-2/3}(4x^3)\)
- Contestar
-
\(\displaystyle \frac{4x^{1/3}}{3}\)
Ejercicio\(\PageIndex{16}\)
\(\displaystyle \frac{(e^{x+3})^2}{e^{-x}}\)
- Contestar
-
\(\displaystyle e^{3x+6}\)
Ejercicio\(\PageIndex{17}\)
\(\displaystyle \frac{e^{x^2-1}}{e^{x+1}}\)
- Contestar
-
\(\displaystyle e^{x^2-x-2}\)
En ejercicios\(\PageIndex{18}\) -\(\PageIndex{20}\), simplificar y escribir el término dado en forma exponencial.
Ejercicio\(\PageIndex{18}\)
\(\displaystyle \frac{4x-1}{\sqrt[3]{(3x+2)^2}}\)
- Contestar
-
\(\displaystyle (4x-1)(3x+2)^{-2/3}\)
Ejercicio\(\PageIndex{19}\)
\(\displaystyle \sqrt[3]{\Bigg(\frac{e^{4\theta-6}y^2}{e^{\theta}y^{-4}}\Bigg)}\)
- Contestar
-
\(\displaystyle e^{\theta-2}y^2, y \neq 0\)
Ejercicio\(\PageIndex{20}\)
\(\displaystyle \sqrt[4]{\Bigg(\frac{x^2y^5}{y^{-3}}\Bigg)^2}\)
- Contestar
-
\(\displaystyle xy^4, y\neq 0\)