🧮 algebra

1. The problem is to express the fraction \(\frac{1}{2}\) in a clear way. 2. \(\frac{1}{2}\) means one part out of two equal parts.

1. Stating the problem: Simplify the expression $$\frac{(9 \times 3^2)^3}{(3 \times 27)^2}$$. 2. Simplify inside the parentheses.

1. Let's start with the first expression: \(2^7 \times 2^4 \times 2^{-8}\). 2. When multiplying powers with the same base, add the exponents:

1. **Problem (a):** Sundip buys 30 litres of fuel at £1.50 per litre and pays the exact amount using three bank notes of £5, £10, £20, or £50. 2. Calculate the total cost of fuel:

**Problem:** Write Leo's time as a fraction of Eve's time and simplify the fraction.

1. **Stating the problem:** We have a sequence of terms $T_1, T_2, \\ldots, T_6$ given as $0, 4, 8, 12, 0, 16$ respectively. 2. We need to find the smallest index $k$ such that $T_

1. Problem (a): Simplify the expression $4x - 3y + x + 7y$. Step 1: Group like terms.

1. We start with Bottle A containing 1.5 litres of water and Bottle B containing 100 millilitres of water. 2. Convert 1.5 litres to millilitres because we need to work in the same

1. **Stating the problem:** We want to calculate the product of the fraction $\frac{2}{7}$ multiplied by $-28$. 2. **Rewrite the expression:** The problem is

1. Énonçons le problème : développer et réduire l'expression $$ (5\sqrt{5} - 4)(5\sqrt{5} - (-4)) $$. 2. Simplifions l'expression dans la deuxième parenthèse : $$ 5\sqrt{5} - (-4)

1. We are asked to simplify the expression $$\frac{+36}{+6}$$. 2. Both numerator and denominator have a positive sign, which means the fraction is positive.

1. Le problème est de simplifier la racine carrée de la fraction $\frac{49}{49}$. 2. On utilise la propriété que $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ pour $a,b > 0$.

1. Énoncé du problème : Développer et réduire l'expression $$ (\sqrt{3} + 2)^2 $$. 2. Commencer par appliquer la formule de développement du carré d'une somme : $$ (a + b)^2 = a^2

1. Énoncé du problème : Calculer $\left(3\sqrt{11} + 3\right)\left(2\sqrt{11} + 2\right)$ et donner la réponse sous la forme $a + b\sqrt{c}$ où $a,b$ sont des nombres entiers ou fr

1. Stating the problem: Calculate the result of the division $+16 \div +8$. 2. Division of two positive numbers: When dividing two positive numbers, the result is also positive.

1. Énonçons le problème : Simplifier l'expression $$3\sqrt{5} \times (-4)\sqrt{8}$$ en une forme du type $$a\sqrt{b}$$ ou un entier/fraction si possible. 2. Réécrivons l'expression

1. Énonçons le problème : calculer $$2\sqrt{275} + 2\sqrt{44} + \sqrt{891}$$ et simplifier l'expression. 2. Factorisons les radicaux pour extraire les carrés parfaits.

1. **State the problem:** Solve the system of linear equations: $$2x + y - z + 3t = 5$$

1. The problem is to simplify the expression $(-15) \times \left(+ \frac{3}{5}\right)$.\n2. First, multiply the numbers ignoring the sign: $15 \times \frac{3}{5} = \frac{15 \times

1. We are asked to simplify and evaluate the expression $$4^{2020} + 2^{2017} - 15.$$\n\n2. Notice that $$4^{2020} = (2^2)^{2020} = 2^{4040}.$$\n\n3. So the expression becomes $$2^

Problem: Solve for $x$ given $x^{-1/3} = y$. 1. Observe the expression and rewrite the power in root form to understand it better.