🧮 algebra

1. **State the problem:** Simplify the expression $$\sqrt[3]{\frac{18}{128}}$$. 2. **Recall the cube root property:** The cube root of a fraction is the fraction of the cube roots,

1. **State the problem:** Simplify the expression $$\sqrt[3]{\frac{18}{125}}$$. 2. **Recall the cube root property:** The cube root of a fraction is the fraction of the cube roots,

1. **State the problem:** Simplify the expression $$\sqrt{2} \cdot \frac{\sqrt{2}}{3} + \sqrt{3} \cdot \frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3}$$. 2. **Reca

1. The problem is to understand the steps from the left term to the right term. 2. Since the user did not provide explicit expressions, I cannot show exact algebraic steps.

1. The problem is to understand how to transform the term on the left side of an equation or expression into the term on the right side. 2. Generally, this involves applying algebr

1. **State the problem:** Expand the expression $ab^3 c^4$ using multiplication. 2. **Recall the rules:** When variables are multiplied, write them together with multiplication sym

1. **State the problem:** Solve the equation $$a(x - 1) - \frac{1 - 2x^2}{2} = (x - 4)(4 + x) + 3(1 + a)$$ for $a$ when $x = -\frac{7}{2}$.\n\n2. **Substitute $x = -\frac{7}{2}$ in

1. **State the problem:** Solve the equation $$(x - 1)^3 + \frac{3}{2}(2x + 3)^2 + (-1 - x)^3 = 18x.$$\n\n2. **Rewrite the equation:** Note that $(-1 - x)^3 = -(x + 1)^3$. So the e

1. **Stating the problem:** Simplify the expression $$\frac{x^{\frac{2}{3}}}{x^{\frac{1}{3}}}$$ and express it in the form $$x^a$$. 2. **Formula used:** When dividing powers with t

1. **State the problem:** Solve the equation $$\frac{\left(2x - \frac{1}{3}\right)(3 - x)}{5} + \frac{(2x + 1)^2}{10} + \left(\frac{1}{10} - \frac{1}{5}\right)^{-1} \left(\frac{x}{

1. **State the problem:** Solve the equation $$1.1 \times 10^{-12} - 2x^3 - 0.2x^2 = 0$$ for $x$. 2. **Rewrite the equation:** Move all terms except the constant to the right side:

1. **State the problem:** Solve the equation $$\frac{7}{12}x + \frac{10x - 15}{3} - x = \frac{4(2x - 1)}{3} - \frac{3(2 - x)}{4}$$ for $x$. 2. **Identify the goal:** We want to iso

1. Let's solve the first algebraic expression: $x + 142 = 16x + 7$. 2. The goal is to isolate $x$ on one side. Start by moving all $x$ terms to one side and constants to the other:

1. **State the problem:** Solve the equation $1.1 \times 10^{-12} = 2x^2(x + 0.1)$ for $x$. 2. **Rewrite the equation:**

1. **State the problem:** Solve the equation $$-\frac{(2-3y)^2}{54} = 0.666\ldots y + \frac{(y+0.5)(0.3333\ldots - y)}{6}$$ for $y$. 2. **Rewrite repeating decimals as fractions:**

1. **State the problem:** Simplify the expression $$7 - \frac{5^2 + 3}{(-1)^2}$$ using order of operations. 2. **Recall order of operations:** Parentheses, Exponents, Multiplicatio

1. **State the problem:** Simplify the expression $2 + 1^3 \times 10 - 3$ using the order of operations. 2. **Recall the order of operations:** Parentheses, Exponents, Multiplicati

1. Proporcionalidade Direta entre t e N: 1.1. Dado que $t$ e $N$ são diretamente proporcionais, temos a relação $N = k t$, onde $k$ é a constante de proporcionalidade.

1. **State the problem:** We are given the function $$y = \frac{4}{x} + \sqrt{x} + 0.2 - 5x$$ and the value $$x = \frac{4}{5}$$.

1. **State the problem:** Solve the equation $2x + 3 = 7$ for $x$. 2. **Use the formula:** To solve a linear equation of the form $ax + b = c$, isolate $x$ by subtracting $b$ from

1. **State the problem:** Evaluate the logarithmic expression $$\log_3 27 - \log_2 4$$. 2. **Recall the logarithm rules:**