🧮 algebra

1. **State the problem:** We need to find the value of $h$ such that $$4^8 \times 8^{12} = 2^h.$$\n\n2. **Rewrite the bases as powers of 2:**\n- $4 = 2^2$\n- $8 = 2^3$\n\n3. **Subs

1. **بيان المسألة:** لدينا متتالية حسابية $(U_n)$ حيث الحد الأول $U_0$ والأساس $r$. المعطيات: $$U_2 - U_0 = 4$$

1. **Problem Statement:** Determine the slope and intercepts of the linear equation $3x + 2y = 12$ using substitution. 2. **Formula and Rules:**

1. The problem is to graph the function $f(x) = \sqrt{x + 4}$ and plot four points on it, including the leftmost point. 2. The function $f(x) = \sqrt{x + 4}$ is defined for $x + 4

1. مسئله: محاسبه مقدار عبارت $(-1)^3 \times 1^6$ است. 2. قانون توان: هر عددی به توان 1 برابر خود عدد است و توان‌های دیگر با ضرب‌های متوالی تعریف می‌شوند.

1. مسئله: مقدار عبارت $$\sqrt[7]{\sqrt{13} + \sqrt{5}} \times \sqrt[7]{18 - 7 \sqrt{5}}$$ را بیابید. 2. قانون استفاده شده: ضرب دو رادیکال با ریشه هفتم برابر است با رادیکال هفتم حاص

1. **Problem Statement:** We are given the quadratic function $$y = -2x^2 + 2x + 24$$ defined for $$-4 \leq x \leq 4$$.

1. **Problem:** Calculate $5 \times 7 \times 2$ using the Commutative or Associative Property. 2. **Formula and Properties:**

1. **State the problem:** We need to find the value of $t$ given the formula $t = k(4k + n)$ with $k = -2$ and $n = 13$. 2. **Write the formula:**

1. **Problem Statement:** Ravi had some money in Rs. 100 notes. He exchanged all these Rs. 100 notes for Rs. 500 and Rs. 200 notes in the ratio 2:3. The total amount of money remai

1. The problem is to simplify the expression $\frac{9^9}{9^2}$.\n\n2. We use the rule of exponents that states $\frac{a^m}{a^n} = a^{m-n}$ when the bases are the same.\n\n3. Applyi

1. The problem is to simplify the expression $\frac{8^7}{8^5}$.\n\n2. We use the rule of exponents that states $\frac{a^m}{a^n} = a^{m-n}$ when the bases are the same.\n\n3. Applyi

1. The problem is to simplify the expression $14^5 \times 8^5$. 2. We use the property of exponents that states $a^n \times b^n = (a \times b)^n$.

1. The problem is to simplify the expression $14^5 \times 8^5$. 2. We use the property of exponents that states $a^m \times b^m = (a \times b)^m$.

1. **State the problem:** We need to complete the tables of values for the lines $y=\frac{1}{4}x+5$ and $y=-2x+\frac{1}{2}$, plot them, and then solve the simultaneous equations gr

1. The problem is to simplify the expression $m \times m^5$. 2. Recall the rule of exponents: when multiplying powers with the same base, add the exponents. That is, $a^x \times a^

1. **State the problem:** Calculate $12^3 \times 12^2$. 2. **Formula used:** When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$

1. **State the problem:** Calculate $3^4 \times 3^7$. 2. **Formula used:** When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$

1. **State the problem:** Find the equation of line N passing through points $(-2, -30)$ and $(0, 10)$ in the form $y = mx + c$. 2. **Formula used:** The slope $m$ of a line throug

1. **State the problem:** Simplify the expression $$\frac{7^8 \times 7^4}{7^2}$$ and express it in the form $$7^a$$. 2. **Recall the exponent rules:**

1. The problem asks us to find the value of $r$ in the equation $$\frac{5^6 \times 5^{10}}{5^2} = 5^r.$$\n\n2. We use the laws of exponents: when multiplying powers with the same b