🧮 algebra

1. **State the problem:** Calculate the value of the expression $$10^4 - 10^3 + 10^0$$. 2. **Recall the powers of 10:**

1. **Stating the problem:** We need to find the value of $n$ in the equation $5.62 \times 10^n = 0.0562$.

1. The problem is to calculate the value of $(-50)^3$. 2. The formula for raising a number to a power is $a^n = a \times a \times \cdots \times a$ (n times).

1. Énoncé du problème : Calculer la valeur de l'expression $$ (4^2 - 2) \times 5 + 4 $$ et donner la réponse sous forme d'un entier relatif. 2. Rappel des règles :

1. **Énoncé du problème** : Calculer la valeur de l'expression $9 - 5 \times 5^2$ et donner la réponse sous forme d'un entier relatif. 2. **Rappel des règles** :

1. The problem is to simplify the expression $10^2 \times 10^5$. 2. We use the rule of exponents that states when multiplying powers with the same base, we add the exponents: $$a^m

1. Énoncé du problème : Calculer la valeur de l'expression $$7 \times 10^{2} + 2 \times 10^{1} + 3 \times 10^{0} + 7 \times 10^{-1}$$ et donner la réponse sous forme d'un entier re

1. **State the problem:** Simplify the expression $7^6 \times 7^4$. 2. **Formula used:** When multiplying powers with the same base, use the rule:

1. Énoncé du problème : Résoudre l'équation $x \times 10^{-2} = 1,1$ pour $x$. 2. Rappel de la règle des puissances : $10^{-2} = \frac{1}{10^2} = \frac{1}{100} = 0,01$.

1. **State the problem:** We are given the equation $\frac{\log x}{\log 2} = -0.515$ and need to find the value of $x$. 2. **Recall the formula:** The expression $\frac{\log x}{\lo

1. Problema: Calculați suma numerelor întregi date. 2. Formula folosită: Pentru adunarea numerelor întregi, dacă semnele sunt aceleași, adunăm valorile absolute și păstrăm semnul c

1. Problema: Calculați expresiile cu radicali. 2. Formula și reguli: Pentru a aduna sau scădea termeni cu radicali, trebuie să avem același radical (radicalul și indicele să fie id

1. The problem is to solve a system of simultaneous linear equations. 2. The general form of simultaneous linear equations is:

1. **State the problem:** Simplify the expression $$\frac{x^5 y^{-6}}{x^{10} y^8}$$ and express it in the form $$\frac{1}{x^{?} y^{_}}$$. 2. **Recall the rule for dividing powers w

1. **State the problem:** Simplify the expression $$\frac{x^2 y^3}{x^9 y^{-6}}$$ and express it in the form $$\frac{y^{[?]}}{x^{[?]}}$$. 2. **Recall the division rule for exponents

1. **State the problem:** We are given two numbers whose product is 814.2, and the smallest number is 23.6. We need to find the sum of these two numbers. 2. **Identify the known va

1. **State the problem:** We are given that the product of two numbers is 814.2 and the smallest number is 23.6. We need to find the sum of these two numbers. 2. **Identify the kno

1. **State the problem:** Simplify the expression $$(4g^5)^2$$. 2. **Recall the power of a product rule:** When raising a product to a power, raise each factor to that power separa

1. **State the problem:** Simplify the expression $$(4h^5)^3$$. 2. **Recall the power of a product rule:** When raising a product to a power, raise each factor to that power separa

1. The phrase "sum of" in mathematics means addition, not multiplication. 2. When you see "sum of" two or more numbers or expressions, it means you add them together.

1. **State the problem:** We need to solve the expression $$\frac{20.46}{16.67 - 13.319}$$. 2. **Understand the formula:** This is a division problem where the numerator is 20.46 a