🧮 algebra

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

1. The problem asks to find the value of $u$ in the equation $$9^{12} = 3^u.$$\n\n2. We start by expressing 9 as a power of 3 because both sides should have the same base to compar

1. **State the problem:** Solve the equation $$2(2x - 8) = 3(4 - x)$$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. **Problem statement:** We need to find how long the temperature held steady based on the graph of temperature over time. 2. **Understanding the graph:** The temperature rises, s

1. Diberikan pola bilangan: 2, 9, 20, 35, 54, ... 2. Kita diminta menentukan suku ke-6 dari pola tersebut.

1. **State the problem:** Solve for $y$ in the equation $$e^{y + 5} = 5$$ and round the answer to the nearest hundredth. 2. **Recall the formula and rules:** To solve for $y$ when

1. Problem: Identify the pattern of the sequence 2, 5, 10, 17, 26, ... and explain the reasoning. 2. The sequence is given as: 2, 5, 10, 17, 26, ...

1. **State the problem:** Solve the equation $4p + 5 = 29 - 2p$ for $p$. 2. **Write down the equation:**

1. **State the problem:** Solve the equation $19 - 4x = 2x + 1$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Simplify the expression $-5i(3 + 6i)$ and express the answer in terms of $i$. 2. **Recall the rule:** When multiplying complex numbers, distribute and use

1. The problem asks to perform the operation and simplify the expression $(5i)^2$ where $i$ is the imaginary unit. 2. Recall that $i$ is defined as $i^2 = -1$.

1. Stating the problem: We need to multiply the complex numbers $11i$ and $-3i$. 2. Recall the rule for multiplying complex numbers: When multiplying, multiply the coefficients and

1. The problem is to simplify the expression $\sqrt{-8} \cdot \sqrt{-200}$.\n\n2. Recall the property of square roots: $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$, which holds for

1. **State the problem:** Express $-3\sqrt{-100}$ as a complex number. 2. **Recall the rule for square roots of negative numbers:** For any positive number $a$, $\sqrt{-a} = \sqrt{