Acceso
Prima
Hogar Banco de preguntas Matemáticas Álgebra
Pregunta
upstudy study bank question image url

b. \( \left(y^{3}\right)^{5} \cdot\left(z^{2}\right)^{4} \)

Ask by Estrada Klein. in Colombia
Mar 15,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

La expresión simplificada es \( y^{15} \cdot z^8 \).

Solución

¡Inicia sesión para desbloquear respuestas gratis!

Una plataforma de aprendizaje en la que confían millones de estudiantes y profesores reales.

star-icon Descubrir

Respondido por UpStudy AI y revisado por un tutor profesional

The Deep Dive

Let’s simplify the expression. When you raise a power to a power, you multiply the exponents. So, we have: \[ \left(y^{3}\right)^{5} = y^{3 \cdot 5} = y^{15} \] Likewise for \(z\): \[ \left(z^{2}\right)^{4} = z^{2 \cdot 4} = z^{8} \] Now, combine the two results: \[ y^{15} \cdot z^{8} \] So the simplified expression is \(y^{15} z^{8}\). Here you have a dazzling combination of powers that showcases the magic of exponent rules!

preguntas relacionadas

Question 4 (1 point) State the total number of complex roots, the possible number of real and imaginary roots and the possible rational roots for each equation. Then find all roots. \( \begin{array}{l}x^{3}+3 x^{2}-x-3=0 \\ \text { a of complex roots: } 3 \\ \text { Possible \# of real roots: } 3 \text { or } 1 \\ \text { Possible \# of imaginary roots: } 2 \text { or } 0 \\ \text { Possible rational roots: } \pm 1, \pm 3 \\ \text { Roots: }\{-3,1,-1\} \\ \text { \# of complex roots: } 3 \\ \text { Possible \# of real roots: } 3 \text { or } 1 \\ \text { Possible \# of imaginary roots: } 2 \text { or } 0 \\ \text { Possible rational roots: } \pm 1, \pm 3 \\ \text { Roots: }\{3,1,-1\} \\ \text { \# of complex roots: } 3 \\ \text { Possible \# of real roots: } 3 \text { or } 1 \\ \text { Possible \# of imaginary roots: } 2 \text { or } 0 \\ \text { Possible rational roots: } \pm 1, \pm 3 \\ \text { Roots: }\{-3,-1,-1\} \\ \text { \# of complex roots: } 3 \\ \text { Possible \# of real roots: } 3 \text { or } 1 \\ \text { Possible \# of imaginary roots: } 2 \text { or } 0 \\ \text { Possible rational roots: } \pm 1, \pm 3 \\ \text { Roots: }\{3, \text { double root at } 1\}\end{array} \) \( \begin{array}{l}\text { d }\end{array} \)
Álgebra United States Mar 17, 2025
Question 6 (1 point) state the total number of complex roots, the possible number of real and imaginary roots and the possible rational roots for each equation. Then find all roots. \[ x^{3}-2 x^{2}-3 x+6=0 \] a \# of complex roots: 6 Possible \# of real roots: 3 or 1 Possible \# of imaginary roots: 2 or 0 Possible rational roots: \( \pm 1, \pm 2 \pm 3, \pm 6 \) Roots: \( -1, \pm \sqrt{3} \) b \# of complex roots: 6 Possible \# of real roots: 3 or 1 Possible \# of imaginary roots: 2 or 0 Possible rational roots: \( \pm 1, \pm 2 \pm 3, \pm 6 \) Roots: \( 2, \pm \sqrt{3} \) c \# of complex roots: 3 Possible \# of real roots: 3 or 1 Possible \# of imaginary roots: 2 or 0 Possible rational roots: \( \pm 1, \pm 2 \pm 3, \pm 6 \) Roots \( 2, \pm \sqrt{3} \) d \# of complex roots: 3 Possible \# of real roots: 3 or 1 Possible \# of imaginary roots: 2 or 0 Possible rational roots: \( \pm 1, \pm 2 \pm 3, \pm 6 \) Roots: \( -1, \pm \sqrt{3} \)
Álgebra United States Mar 17, 2025
Summarize all pertinent information obtained by applying the graphing strategy and sketch the graph of \( y=f(x) \). \[ f(x)=\frac{x^{2}+13 x+36}{x^{2}+8 x+16} \] tina the aomain or \( \mathrm{r}(\mathrm{X}) \). seiect the correct cnoice deiow ana, it necessary, till in the answer dox to complete your cnoice. A. The domain is all real \( x \), except \( x= \) \( \square \) (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. The domain is all real \( x \). Find the \( x \)-intercepts of \( f(x) \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The \( x \)-intercept(s) is/are at \( x= \) \( \square \) . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no \( x \)-intercepts. Find the \( y \)-intercepts of \( f(x) \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Álgebra United States Mar 17, 2025
3. Write out Cayley tables for groups formed by the symmetries of a rectangle and for \( \left(\mathbb{Z}_{4 y},+\right) \). How many elements are in each group? Are the groups the same? Why or why not?
Álgebra United States Mar 17, 2025
Question 3 (1 point) Using technology and the remainder theorem, find the actual rational zeros of the fun \[ f(x)=x^{3}-14 x^{2}+59 x-70 \] a \( -2,-5,-7 \) b \( 2,5,7 \) c \( \pm 1, \pm 14, \pm 59, \pm 70 \) d \( 1,-14,59,-70 \)
Álgebra United States Mar 17, 2025

Latest Algebra Questions

3. Write out Cayley tables for groups formed by the symmetries of a rectangle and for \( \left(\mathbb{Z}_{4 y},+\right) \). How many elements are in each group? Are the groups the same? Why or why not?
Álgebra United States Mar 17, 2025
himpunan penyelesaian dari sistem persamaan \( 2 x+2 y=4 \) dan \( 3 x+y=6 \) adalah
Álgebra Indonesia Mar 17, 2025
Question 4 (1 point) State the total number of complex roots, the possible number of real and imaginary roots and the possible rational roots for each equation. Then find all roots. \( \begin{array}{l}x^{3}+3 x^{2}-x-3=0 \\ \text { a of complex roots: } 3 \\ \text { Possible \# of real roots: } 3 \text { or } 1 \\ \text { Possible \# of imaginary roots: } 2 \text { or } 0 \\ \text { Possible rational roots: } \pm 1, \pm 3 \\ \text { Roots: }\{-3,1,-1\} \\ \text { \# of complex roots: } 3 \\ \text { Possible \# of real roots: } 3 \text { or } 1 \\ \text { Possible \# of imaginary roots: } 2 \text { or } 0 \\ \text { Possible rational roots: } \pm 1, \pm 3 \\ \text { Roots: }\{3,1,-1\} \\ \text { \# of complex roots: } 3 \\ \text { Possible \# of real roots: } 3 \text { or } 1 \\ \text { Possible \# of imaginary roots: } 2 \text { or } 0 \\ \text { Possible rational roots: } \pm 1, \pm 3 \\ \text { Roots: }\{-3,-1,-1\} \\ \text { \# of complex roots: } 3 \\ \text { Possible \# of real roots: } 3 \text { or } 1 \\ \text { Possible \# of imaginary roots: } 2 \text { or } 0 \\ \text { Possible rational roots: } \pm 1, \pm 3 \\ \text { Roots: }\{3, \text { double root at } 1\}\end{array} \) \( \begin{array}{l}\text { d }\end{array} \)
Álgebra United States Mar 17, 2025
Summarize all pertinent information obtained by applying the graphing strategy and sketch the graph of \( y=f(x) \). \[ f(x)=\frac{x^{2}+13 x+36}{x^{2}+8 x+16} \] tina the aomain or \( \mathrm{r}(\mathrm{X}) \). seiect the correct cnoice deiow ana, it necessary, till in the answer dox to complete your cnoice. A. The domain is all real \( x \), except \( x= \) \( \square \) (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. The domain is all real \( x \). Find the \( x \)-intercepts of \( f(x) \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The \( x \)-intercept(s) is/are at \( x= \) \( \square \) . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no \( x \)-intercepts. Find the \( y \)-intercepts of \( f(x) \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Álgebra United States Mar 17, 2025
State the total number of complex roots, the possible number of real and imaginary roots and the possible rational roots for each equation. Then find all roots. \[ x^{3}-1=0 \] a \# of complex roots: 3 Possible \# of real roots: 3 or 1 Possible \# of imaginary roots: 2 or 0 Possible rational roots: \( \pm 1 \) \[ \text { Roots: } \pm 1, \frac{-1+i \sqrt{3}}{2} \] b \[ 1, \frac{-1+i \sqrt{3}}{2}, \frac{-1-i \sqrt{3}}{2} \text { \# of complex roots: } 3 \] Possible \# of real roots: 3 or 1 Possible \# of imaginary roots: 2 or 0 Possible rational roots: \( \pm 1 \) Roots: c \# of complex roots: 3 Possible \# of real roots: 3 or 1 Possible \# of imaginary roots: 2 or 0 Possible rational roots: \( \pm 1 \) \[ \text { Roots: }-1, \frac{-1+i \sqrt{2}}{5}, \frac{-1-i \sqrt{2}}{5} \] d \# of complex roots: 3 Possible \# of real roots: 3 or 1 Possible \# of imaginary roots: 2 or 0 Possible rational roots: \( \pm 1 \) Roots: \[ -1, \frac{i \sqrt{3}}{2}, \frac{-i \sqrt{3}}{2} \]
Álgebra United States Mar 17, 2025
Anterior Próximo
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde Hazte Premium
Estudiar puede ser una verdadera lucha
¿Por qué no estudiarlo en UpStudy?
Seleccione su plan a continuación
Prima

Puedes disfrutar

Empieza ahora
  • Explicaciones paso a paso
  • Tutores expertos en vivo 24/7
  • Número ilimitado de preguntas
  • Sin interrupciones
  • Acceso completo a Respuesta y Solución
  • Acceso completo al chat de PDF, al chat de UpStudy y al chat de navegación
Básico

Totalmente gratis pero limitado

  • Solución limitada
Bienvenido a ¡Estudia ahora!
Inicie sesión para continuar con el recorrido de Thoth AI Chat
Continuar con correo electrónico
O continuar con
Al hacer clic en "Iniciar sesión", acepta nuestros términos y condiciones. Términos de Uso & Política de privacidad