🧮 algebra

1. The problem is to simplify or understand the expression $\frac{1}{ix^{199}}$. 2. Here, $i$ is the imaginary unit where $i^2 = -1$, and $x^{199}$ is $x$ raised to the 199th power

1. The problem is to simplify the expression $-58 / -2$. 2. Division of two negative numbers results in a positive number.

1. The problem is to simplify the expression $\frac{1}{i^2}$.\n\n2. Recall that $i$ is the imaginary unit, defined by $i^2 = -1$.\n\n3. Substitute $i^2$ with $-1$ in the expression

1. The problem is to multiply two numbers: $-24$ and $-6$. 2. When multiplying two negative numbers, the result is positive.

1. **State the problem:** We have an arithmetic sequence where the first term $a_1=2$ and the fifth term $a_5=18$. We need to find the sixth term $a_6$. 2. **Recall the formula for

1. **State the problem:** We are given a green line segment approximately passing through points (0,9) and (9,4). We need to find the slope of this original line and then find the

1. The problem is to multiply 17 by -3. 2. Multiplication of a positive number by a negative number results in a negative number.

1. The problem states that the first term $a_1$ of a geometric sequence is 2 and the second term $a_2$ is 6. 2. Recall that in a geometric sequence, each term is found by multiplyi

1. **State the problem:** We are given two lines on a coordinate plane. We need to find the slope of the original line (green) and the slope of a line perpendicular to it (blue). 2

1. The problem states that the first term of an arithmetic sequence is 3 and the second term is 15. 2. Recall that in an arithmetic sequence, the difference between consecutive ter

1. **State the problem:** We are given a line and need to find its slope and the slope of a line perpendicular to it. 2. **Identify the given line:** The green line passes through

1. **State the problem:** We are given the geometric sequence 18, 54, 162, 486, ... and need to find the first term and the term-to-term rule. 2. **Identify the first term:** The f

1. The problem is to find the product of $-12$ and $-8$. 2. When multiplying two negative numbers, the result is positive.

1. The problem asks to find the slope of the given line and the slope of a line perpendicular to it. 2. The given line descends from approximately (-10, 2) to (10, -8).

1. **Statement of the problem:** Simplify the expression $$B = \frac{(-4)^3 \times (-6)^4 \times 2^5 \times (-27)^{-2}}{(-9)^3 \times 6^8} \times (-18)^{-4}$$

1. **State the problem:** We need to find the least integer value of $x$ that satisfies the inequality $$\frac{5x - 3}{2} > 5.$$\n\n2. **Isolate the variable:** Multiply both sides

1. The problem asks for a number that is both a square number and an even number. 2. A square number is a number that can be expressed as $n^2$ where $n$ is an integer.

1. **State the problem:** We need to make $a$ the subject of the formula given by $$b^3 = \frac{4(8d - 3a)}{9}$$

1. The problem is to find the cube root of 64. 2. The cube root of a number $x$ is a number $y$ such that $y^3 = x$.

1. **التمرين الأول: تصنيف الأعداد** - A = $\frac{\sqrt{48} - 4\pi}{2\pi - \sqrt{12^7}}$

1. **State the problem:** Expand and simplify the expression $$(x + 5)(x - 3)(2x - 1)$$. 2. **First, expand the first two binomials:**