🧮 algebra

1. **Problem:** Simplify the expression $6^7 \cdot 6^9$ and verify if it equals $6^{16}$. 2. **Formula:** When multiplying powers with the same base, add the exponents: $$a^m \cdot

1. **State the problem:** Solve the equation $$15y + 5y^3 + 3y^5 = 5x^3$$ for $y$ in terms of $x$. 2. **Rewrite the equation:**

1. The problem involves simplifying expressions with rational exponents and radicals. 2. Recall the key rule: $$a^{\frac{m}{n}} = \sqrt[n]{a^m} = (\sqrt[n]{a})^m$$ where $a$ is the

1. **State the problem:** Solve the equation $$(1 + \ln x)^2 = 0$$ for $x$. 2. **Understand the equation:** The square of a quantity equals zero only if the quantity itself is zero

1. **Stating the problem:** Simplify the expression $$\frac{25x^7}{-5x^2}$$ using the laws of exponents. 2. **Formula and rules:**

1. **State the problem:** Simplify the expression $$\frac{25x^7}{-5x^2}$$. 2. **Recall the laws of exponents and division:** When dividing powers with the same base, subtract the e

1. The problem involves applying the laws of exponents to simplify expressions. 2. Recall the key exponent rules:

1. **State the problem:** Simplify the expression $$\frac{25x^7}{-5x^2}$$ using the laws of exponents. 2. **Recall the laws of exponents:**

1. Das Problem ist, ein Gleichungssystem mit der Methode des Gleichsetzens zu lösen. 2. Die Methode des Gleichsetzens besteht darin, beide Gleichungen nach derselben Variablen aufz

1. **Problem statement:** We have two wine packages with different numbers of bottles and total prices. We want to find the price of one bottle of red wine and one bottle of white

1. The problem is to find the expression for $v_{n+1} - v_n$. 2. This represents the difference between the term at position $n+1$ and the term at position $n$ in a sequence $\{v_n

1. **Énoncé du problème :** Nous devons préciser le sens de variation de la suite $(v_n)$ définie par $v_n = \frac{u_n - 1}{u_n + 3}$.

1. **State the problem:** Simplify the algebraic expression $$\frac{5}{8}x + \frac{3}{4}y + \frac{1}{2}x - \frac{1}{4}y$$. 2. **Identify like terms:** Terms with $x$ are $$\frac{5}

1. **State the problem:** Solve the equation $3n - 4 = 11$ for $n$. 2. **Formula and rules:** To solve for $n$, we need to isolate $n$ on one side of the equation by performing inv

1. **State the problem:** Solve the equation $2n + 5 = 13$ for $n$. 2. **Use the formula:** To solve linear equations, isolate the variable by performing inverse operations.

1. **State the problem:** Hannah needs to drive 312 miles home and wants to know how much it will cost to fill up her gas tank based on the regression equation derived from her gas

1. **Problemstellung:** Vereinfache den Ausdruck $$\sqrt{2x^3 \sqrt{8x^2 \cdot (x\sqrt{2})^2}}$$. 2. **Formeln und Regeln:**

1. **State the problem:** Simplify the expression $5a(a-3)-2a(a+4)$. 2. **Write the expression:** $5a(a-3)-2a(a+4)$.

1. **Problem:** Simplify the expression $2x(2x - 6) - 3x(x + 5)$. 2. **Formula and rules:** Use the distributive property $a(b + c) = ab + ac$ to expand each term.

1. **State the problem:** Simplify or understand the expression $$\frac{5+x}{12+x}$$. 2. **Formula and rules:** This is a rational expression, a fraction where numerator and denomi

1. **Planteamiento del problema:** Tenemos dos depósitos, A y B, donde A se vacía y B se llena simultáneamente. Se nos dan dos gráficas lineales: una decreciente (azul) y otra crec