🧮 algebra

1. **Stating the problem:** We want to disprove the statement: "If $a,b \notin \mathbb{Q}$ (irrational numbers), then $a^b \notin \mathbb{Q}$ (irrational)." 2. **Understanding the

1. The problem is to simplify the expression $$\frac{(-a)^{41}}{a^5}$$. 2. We use the laws of exponents: $$\frac{x^m}{x^n} = x^{m-n}$$ and $$(-a)^n = (-1)^n a^n$$.

1. The problem is to simplify the expression $$\frac{(40 - a)^5}{a^5}$$. 2. We use the property of exponents that states $$\frac{x^m}{y^m} = \left(\frac{x}{y}\right)^m$$.

1. The problem is to understand the expression $a$ to the power $b$, which is written as $a^b$. 2. The formula for exponentiation is $a^b = \underbrace{a \times a \times \cdots \ti

1. **Stating the problem:** We want to prove that if $a,b \notin \mathbb{Q}$ (i.e., $a$ and $b$ are irrational numbers), then the product $ab$ is also irrational, i.e., $ab \notin

1. **State the problem:** Find the zeros of the function $$f(x) = 2x^3 + 5x^2 - 11x + 4$$. 2. **Formula and rules:** To find zeros, solve $$f(x) = 0$$. For cubic polynomials, try r

1. The problem is to simplify the sum of three binary numbers: $1101_2 + 101_2 + 11_2$ and convert the result to decimal. 2. Recall that binary numbers are base 2, and to convert a

1. **State the problem:** Find the rational zeros of the polynomial $$f(x) = x^3 - 5x^2 + 2x + 1$$ using the Rational Zero Theorem. 2. **Recall the Rational Zero Theorem:** Possibl

1. The problem is to simplify the expression $1101_2$ which is a binary number. 2. To simplify or understand a binary number, we convert it to decimal (base 10).

1. **State the problem:** Solve for $m$ in the equation $$4^{m+2} + 4^{m+5} = 65.$$\n\n2. **Recall the properties of exponents:** For any base $a$ and exponents $x$ and $y$, $$a^{x

1. **Énoncé du problème :** Développer $P(x)=x^2-9+(x-3)(3x+5)$, résoudre $P(x)=-24$, montrer que $P(x)=4(x-3)(x+2)$, factoriser $Q(x)=(x+2)^2-4x-8$, déterminer les valeurs de $x$

1. **State the problem:** Solve the inequality $$|x^2 - x + 1| \geq 1$$. 2. **Recall the definition of absolute value inequality:** For any expression $A$, $$|A| \geq 1$$ means $$A

1. Problem: Find the month with the highest percentage change in rice price in Kabupaten Sejahtera in 2022. 2. Formula: Percentage change between two months is calculated as

1. The problem is to solve the inequality $|x^2+2| \le 11$. 2. Recall that the absolute value inequality $|A| \le B$ means $-B \le A \le B$.

1. The problem is to find the value of $\lfloor 2.5 \rfloor$. 2. The floor function $\lfloor x \rfloor$ gives the greatest integer less than or equal to $x$.

1. **Problem statement:** We are given the function $b(x) = \frac{3}{3x - 4}$ defined on the interval $\left[\frac{4}{3}, +\infty\right[$. We want to understand its behavior and gr

1. The problem is to evaluate or understand the expression involving the floor function: $\lfloor x \rfloor 2.5$. 2. The floor function $\lfloor x \rfloor$ returns the greatest int

Let's solve the equation step by step! 🎉 1. Here is the equation:

1. The problem is to solve the algebraic expression $3y^3 - 2y^2 + 5y - 6$ by factoring or finding its roots. 2. We use the factoring method to solve cubic expressions. The goal is

1. **Stating the problem:** OSIS MAN IC has a maximum initial capital of 900000 Rupiah to buy one variant of drink in size M or S from Pak Amir. They sell the drinks at 9000 Rupiah

1. The problem is to find the radius $r$ of the 2nd blade given the equation $r(2 + \text{theatre}) = 60$. 2. We start with the equation: