🧮 algebra

1. **State the problem:** Evaluate the expression $4^{-5} \cdot 4^{5}$. 2. **Recall the exponent multiplication rule:** When multiplying powers with the same base, add the exponent

1. **State the problem:** Evaluate the expression $$(-9)^2 \cdot (-9)^2$$. 2. **Recall the formula and rules:** When raising a number to a power, $$a^n$$ means multiplying $$a$$ by

1. **State the problem:** We need to express the equation $8\sqrt{a} = a^n$ in terms of $n$. 2. **Recall the rules:** The square root of $a$ can be written as a fractional exponent

1. **State the problem:** Given the expression $$\sqrt[5]{b^7} = b^m$$, find the value of the exponent $$m$$. 2. **Raise both sides to the power of 5:**

1. **State the problem:** Solve the equation $$a^3 + a^2 = 36$$ for the variable $a$. 2. **Rewrite the equation:** We want to find $a$ such that $$a^3 + a^2 - 36 = 0$$.

1. El problema nos pide identificar la expresión algebraica que representa la función exponencial mostrada en la gráfica. 2. La gráfica muestra una curva exponencial que crece rápi

1. El problema nos pide encontrar un número racional que esté entre dos números racionales dados: $\frac{1}{4}$ y $\frac{5}{2}$.\n\n2. La fórmula para encontrar un número entre dos

1. **Problem:** Solve and analyze the quadratic function $y = x^2 - 4x + 3$. 2. **Formula:** The quadratic function is $y = ax^2 + bx + c$.

1. **Problemstellung:** Wir sollen die Linearfaktordarstellung der quadratischen Funktion $$h(x) = 4x^2 + 3x + \frac{1}{2}$$ bestimmen. 2. **Formel:** Für eine quadratische Funktio

1. **Problemstellung:** Wir sollen die Linearfaktordarstellung der quadratischen Funktion $$h(x) = 4x^2 + 3x + \frac{1}{2}$$ ermitteln, falls möglich. 2. **Formel und Vorgehen:** D

1. The problem is to create a quiz question for you. 2. Since you requested a quiz, here is a simple algebra question:

1. **Problem:** Find the slope of the line through points (2,3) and (4,9). 2. **Formula:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by:

1. The problem is to evaluate the expression $|74|$. 2. The absolute value function $|x|$ returns the non-negative value of $x$ regardless of its sign.

1. Planteamos el problema: Resolver la ecuación $2x + 3 = 7$. 2. Usamos la fórmula para resolver ecuaciones lineales: $ax + b = c \Rightarrow x = \frac{c - b}{a}$.

1. **Problem statement:** You travel a 500 km trip, the car consumes 15 L per 100 km, and oil costs 2 per liter. You can invite up to 4 friends, but each friend adds 10 km to the t

1. **Problem statement:** You travel a base distance of 500 km for a round trip (aller-retour), but each additional friend you invite (up to 5 people including you) adds 10 km to t

1. **Le Camp de Vacances** Énoncé : Le camp loue un chalet pour 1200 par semaine. Chaque enfant inscrit ajoute 100 de frais de personnel. Maximum 20 enfants.

1. The problem asks to redo all the numbers but provide the formula as the final answer instead of a numeric value. 2. Generally, when solving algebraic problems, we use formulas t

1. **Problem statement:** You travel a base distance of 500 km for a round trip (aller-retour), but each additional friend adds 10 km to the trip. The car consumes 15 L of fuel per

1. **State the problem:** Solve the equation $$\frac{2}{3}x = 8$$ for $x$. 2. **Formula and rules:** To solve for $x$, multiply both sides of the equation by the reciprocal of the

1. **Stating the problem:** We need to solve the equation $2x + 3 = 11$ for $x$. 2. **Formula and rules:** To solve a linear equation, we isolate the variable on one side by perfor