🧮 algebra

1. Simplify the expression \( \frac{12 a^0 b^3 c^{-1}}{15 a^{-2} b^5 c^{-3}} \). 2. Simplify the expression \( \frac{(3 x y^{-2})^{-2}}{3 x^{-2} y} \).

1. **State the problem:** Evaluate and express in standard form the sum $$(7.01 \times 10^6) + (5 \times 10^5).$$ 2. **Recall the rule:** To add numbers in scientific notation, the

1. Simplify the expression \(\frac{12a^0 b^3 c^{-1}}{15 a^{-2} b^5 c^{-3}}\). 2. Simplify the expression \(\frac{(3xy^{-2})^{-2}}{3x^{-2} y}\).

1. **Stating the problem:** We are given a sequence where the number of small triangles for Figure 1 is 4, and for Figure 2 is 9. We need to find the number of small triangles for

1. **State the problem:** Evaluate $$\frac{(5 \times 10^{3}) \times (2 \times 10^{-3})}{7}$$ and express the answer in standard form rounded to 2 decimal places. 2. **Use the prope

1. **State the problem:** Simplify the expression $$\frac{(3xy^{-2})^{-2}}{3x^{-2}y}$$. 2. **Recall the rules:**

1. **Énoncé du problème :** Trouver pour quelles valeurs de $x$ la fonction $F(x) = \frac{A(x)}{B(x)}$ existe. 2. **Rappel important :** Une fonction rationnelle $F(x) = \frac{A(x)

1. **State the problem:** Simplify the expression $$\frac{(3xy^{-2})^{-2}}{3x^{-2}y}$$. 2. **Recall exponent rules:**

1. **Problem:** Given two numbers A and B with ratio 3:5 and their sum is 160, find B. 2. **Formula:** If $A:B=3:5$, then $A=3x$ and $B=5x$ for some $x$.

1. The problem is to evaluate the expression $23 - 24$. 2. The subtraction operation means we take 24 away from 23.

1. The problem is to simplify the expression \( \sqrt{x} \), which means finding the principal square root of \( x \). 2. The square root function is defined as \( \sqrt{x} = y \)

1. **State the problem:** Check if the points (1, 2) and (4, 0) are solutions of the equation $x - 2y = 4$. 2. **Recall the rule:** A point $(x, y)$ is a solution to the equation i

1. **State the problem:** Max rounded each number to 1 significant figure and multiplied 20 by 500 to get 10,000. We want to find the smallest possible product of the original numb

1. **State the problem:** We need to find the value of $d$ in the equation $$\frac{x^{24}}{x^{d}} = x^{8}.$$\n\n2. **Recall the exponent division rule:** When dividing powers with

1. **State the problem:** We need to find the ratio of juniors to adults given two ratios: juniors to children is 1:3, and children to adults is 5:2. 2. **Write down the given rati

1. **State the problem:** Amir has 80 coins consisting of £1 and 50p coins in a ratio of 3:2. We need to find the total amount of money in pounds. 2. **Set up variables:** Let the

1. **State the problem:** Simplify the expression $$\frac{6h^{5} \times 4h^{3}}{8h^{15}}$$. 2. **Use the laws of exponents and multiplication:** When multiplying terms with the sam

1. Stating the problem: Calculate $\frac{1}{3} \times \left( \frac{9}{3} + \frac{5}{6} \right)$.\n\n2. Use the order of operations: first solve inside the parentheses, then multipl

1. **State the problem:** We have a quartic equation $$x^4 + bx^3 + cx^2 + dx - 2 = 0$$ with roots $$\alpha, \beta, \gamma, \delta$$.

1. **State the problem:** Simplify the expression $120x^8 + 240x^8 + 360x^8$. 2. **Identify like terms:** All terms have the same variable part $x^8$, so we can add their coefficie

1. **State the problem:** Simplify the expression $120x^8 + 240x^8 + 360x^?$ where the exponent of the last term is unknown. 2. **Identify the terms:** The first two terms are like