🧮 algebra

1. **Stating the problem:** Simplify the expression $$9x^6 y^{\frac{2}{3}} \times 5x^{-5} y^{-\frac{1}{3}}$$. 2. **Combine the numerical coefficients:** Multiply 9 and 5.

1. Simplify $9x^{-6}y^{3} \div 0.5x^{-3}y^{1}$. Step 1: Rewrite division as multiplication:

1. The problem is to simplify the expression $$\frac{-23}{7} \div -\frac{2}{1}$$. 2. Division of fractions can be converted to multiplication by the reciprocal, so we rewrite it as

1. Let's start by stating the problem: Solve for $x$ in the equation $7x + 25 = 11x + 5$. 2. The goal when solving equations is to group like terms together, meaning terms involvin

1. Stating the problem: We have three sets of three numbers each in overlapping hexagons. Set I: 4, 31, 15

1. Let's first understand the problem: we need to find the sum of the series $$20 - 24 + 28 - 32 + \cdots + 204 - 208$$. 2. Notice the pattern: terms alternate between positive and

1. Problema: La temperatura ha subido 18° desde -5°. ¿Cuál es la nueva temperatura? Calculo la temperatura sumando 18 a -5:

1. The user is asking about the fourth power of the variable $y$, written as $y^4$. 2. The expression $y^4$ means $y$ multiplied by itself 4 times, i.e., $$y^4 = y \times y \times

1. Let's state the problem clearly: You want to understand how to work with a first number that is a fraction and a second number that is a whole number. 2. Suppose the first numbe

1. Problem (i): Simplify $$\frac{3x+5}{2x^2-9}$$. The denominator can be factored as $$2x^2-9 = 2x^2 - 9 = 2x^2-9$$ is not factorable using integers.

1. نبدأ بحل الجزء الأول: $$\ln(5 - \sqrt{6})$$. 2. ننتقل للجزء الثاني: $$4 \ln(7 - \sqrt{2})$$، ويمكن استخدام خاصية اللوغاريتم \(a \ln b = \ln(b^a)\) لتحويله إلى $$\ln((7 - \sqrt{2

1. Let's restate the question: You want to know if for any equation where both sides have the same denominator, you can multiply both sides by that denominator (for example, 10) to

1. Énonçons le problème : Calculer les expressions $x = (n+1)^2 + n^2 - 1$ et $y = 4n + 3$ pour $n \in \mathbb{N}$.\n\n2. Développons et simplifions $x$ :\n$$x = (n+1)^2 + n^2 - 1

1. Masalah: Cari nilai $x$ dari persamaan kuadrat $2x^2 - 4x - 6 = 0$.\n\n2. Mulakan dengan menulis semula persamaan: $$2x^2 - 4x - 6 = 0.$$\n\n3. Bahagikan kedua-dua belah dengan

1. Let's start by understanding the problem: We have the equation $$\frac{3x + 1}{10} = 1$$, and we want to find the value of $x$. 2. Think of $10$ as the number of blocks that the

1. **Problem:** GOAL and FCTR are squares. The area of GOAL is $9x^2 - 12x + 4$ cm$^2$ and is larger than the area of FCTR by $5x^2 + 8x - 21$ cm$^2$. Find the length of a side of

1. **Evaluate the expression** $6^{-2} - 4^{-2} - (-8)^{-2} - \frac{1}{36}$ step-byn step. 2. Recall that $a^{-n} = \frac{1}{a^n}$.

1. The problem is to find the function that fits the user's query and to provide a detailed explanation with steps. 2. Here we assume the function is $y=a^x$ with $a>0$ and $a\ne 1

1. **Problem:** GOAL and FCTR are squares. Area of GOAL is given by $$9x^4 - 12x + 4$$ cm² and this area is larger than FCTR's area by $$5x^2 + 8x - 21$$ cm². Find the side length

1. Identifikasi daerah arsiran dan batas-batas sistem pertidaksamaan pada gambar pertama. - Titik-titik penting: (-2,0), (4,0), garis vertikal antara y=2 dan y=4.

1. The problem asks to find the third proportional to the expressions $(x+y)^2$ and $x^2 - xy - 2y^2$. 2. Recall that if $a$, $b$, and $c$ are in proportion, then $\frac{a}{b} = \f