🧮 algebra

1. The problem states the property of radicals: For any real number $n$, the $n$th root of $a^m$ is equal to $a^{m/n}$. 2. The formula used is:

1. The problem asks whether for any real number $n$, the equation $$\sqrt[n]{ab} = \sqrt[n]{a} \times \sqrt[n]{b}$$ is true. 2. The formula used here is the property of radicals: $

1. **State the problem:** We need to determine if the statement "If $n$ is even and $a$ is negative, then the $n$th root of $a$ is not a real number" is true or false. 2. **Recall

1. **State the problem:** Determine if the set $A = \{ f_{a,b} : a,b \in \mathbb{R} \}$ with the operation of composition $(A, \circ)$ forms a monoid, and whether $(A, \circ)$ is a

1. The problem asks whether the statement "An exponent determines how many times the base is multiplied to itself" is true or false. 2. Recall the definition of an exponent: For a

1. The problem asks whether any number raised to the power of 1 is equal to the number itself. 2. The rule for exponents states that for any number $a$, $a^1 = a$.

1. The problem states: "Any number raised to 0 is equal to 1." We want to understand why this is true. 2. The rule for exponents is: $$a^m \times a^n = a^{m+n}$$ where $a$ is any n

1. **State the problem:** Simplify the expression $$21 - \frac{7}{3x} \div \frac{7}{21x - 3}$$. 2. **Recall the division of fractions rule:** Dividing by a fraction is the same as

1. **Problem statement:** Simplify the expressions using the laws of indices. 2. **Recall the laws of indices:**

1. **Problem i.a:** Simplify $\left(3x^5\right)^4$ using the laws of indices. 2. The law of indices states that $(ab)^n = a^n b^n$ and $(x^m)^n = x^{mn}$.

1. The question asks if we solve with variables $p$ and $q$ separately. 2. In algebra or equations involving multiple variables, we often solve for one variable at a time, treating

1. **State the problem:** Solve the inequality $$\frac{2x}{x+1} < -2$$ using the Case Analysis Method. 2. **Rewrite the inequality in the form $$\frac{P(x)}{Q(x)} < 0$$:**

1. The problem asks us to study the inequality $x \leq -4$. 2. The inequality is already given: $x \leq -4$ means $x$ is less than or equal to $-4$.

1. The problem is to check the values or conditions for variables a, b, and c. 2. Since the user did not specify a particular equation or context, we need more information to proce

1. The problem states that variables a, b, and c are incorrect or wrong. 2. To address this, we need to identify what "wrong" means in context: are these variables incorrect values

1. The problem involves understanding the relationships between the original price of a video game, the sale price, the percent of the original price Adam will pay, the percent dis

1. **State the problem:** Arrange the given mathematical expressions from least to greatest. 2. **List the expressions:**

1. Énoncé du problème : Résoudre l'équation $3x^2 + 24x = -45$ par factorisation. 2. Mettons tous les termes d'un côté pour avoir une équation égale à zéro :

1. The problem is to find the value of $60!$, which means the factorial of 60. 2. The factorial of a positive integer $n$, denoted $n!$, is the product of all positive integers fro

1. **State the problem:** Solve for $s$ in the equation $$\frac{-11s - 4}{8} = 5.$$\n\n2. **Use the formula:** To solve for $s$, first eliminate the denominator by multiplying both

1. The problem is to solve the equation $$\frac{6b + 10}{4} = 7$$ for the variable $b$. 2. To solve for $b$, we first eliminate the denominator by multiplying both sides of the equ