🧮 algebra

**Exercise A: Express in exponential form** 1. The expression is ³√64².

1. Express the following in exponential form. 1. $\sqrt[3]{64^2}$ is $64^{\frac{2}{3}}$.

1. Stating the problem: Factorise completely the expression $$4x^{2} + 8xy - xy - 2y^{2}$$. 2. Group terms for easier factoring: $$ (4x^{2} + 8xy) - (xy + 2y^{2}) $$.

1. Stating the problem: Evaluate the expression $\left(\frac{1}{3} + 2, 5\right) \times 40\% - 1 \div 6$. 2. First, clarify the expression. Assuming the comma separates two express

1. **Evaluate** $\log_3 1$\nRecall that $\log_b a$ answers the question: "To what power must we raise $b$ to get $a$?"\nSince $3^0 = 1$, we have $\log_3 1 = 0$.\n\n2. **Evaluate**

1. The problem asks to factorise completely the quadratic expression $$9x^2 - 4$$. 2. Notice this is a difference of squares, which has the general formula $$a^2 - b^2 = (a-b)(a+b)

1. Énonçons le problème : Sami perd successivement les fractions $\frac{1}{4}$, puis $\frac{2}{5}$, puis $\frac{1}{3}$ de ses billes à chaque partie. 2. Appelons $x$ le nombre init

1. Masalah yang diajukan adalah dari mana nilai 0,09 berasal dalam konteks ini. 2. Angka 0,09 biasanya merupakan bentuk desimal dari sebuah pecahan atau hasil perhitungan.

1. **State the problem:** Solve the quadratic equation $$15x^2 + x - 6 = 0$$ by factorization and find $x$. 2. **Factorize the quadratic:** Looking for two numbers that multiply to

1. The function given is $$h(x) = 4\sqrt{-5x^2 + 2x + 1}$$. We need to find the domain where the expression inside the square root is non-negative because the square root of a nega

1. Write the point-slope form for the line with slope $\frac{6}{5}$ through point $(-4,-2)$. Using the formula $y - y_1 = m(x - x_1)$, substitute $m = \frac{6}{5}$, $x_1 = -4$, $y_

1. Given the equation \(\log_3(x + 2) + 4 = 6\), we want to solve for \(x\).\n\n2. Subtract 4 from both sides to isolate the logarithm:\n\n\[\log_3(x + 2) = 6 - 4 = 2\]\n\n3. Recal

1. We start from the original problem and aim to solve it by a different method. 2. Let's assume the original problem is solving the quadratic equation $ax^2 + bx + c = 0$ by the q

1. **State the problem:** Factorise completely the expressions 2x^2y + 6x^2y^2. 2. **Identify common factors:** Both terms have the factor 2x^2y.

1. **Problem statement:** If 978.7 is 100%, find how much 2% is. 2. To find 2%, we use the formula:

1. **State the problem:** Simplify the expressions \(\frac{7 \sqrt{3} + \sqrt{5}}{\sqrt{5} - 2}\) and \(\frac{9 \sqrt{5} + 3}{4 - \sqrt{10}}\). 2. **Simplify the first expression:*

1. Stated problem: Solve the equation $$-1-3(x+1)+4(x-1)(2x+3)=5$$. 2. Expand the terms: $$-1-3x-3 + 4(x-1)(2x+3) = 5$$ simplifies to $$-4 - 3x + 4(x-1)(2x+3) = 5$$.

1. The problem: Simplify the expression $2b$ without using derivatives. 2. Since $2b$ is already a simplified algebraic expression representing two times the variable $b$, no furth

1. **Problem statement:** A 4 ft thick slice is cut off the top of a cube, producing a rectangular box with volume 67 ft\(^3\). We want to find the side length $s$ of the original

1. Problem (a): Find the inverse function $f^{-1}$ of the function $f(x) = -3 + \sqrt{3 + 2x}$ and determine the domain and range of $f^{-1}$. 2. To find the inverse, set $y = f(x)

1. We are asked to find solutions to inequalities by graphing three parabolas and analyzing their vertices and tables of values. 2. For the first inequality: $y > (x-5)^2 + 2$