🧮 algebra

1. **State the problem:** Simplify the expression $$2^{-4} + 2^{-2}$$. 2. **Recall the rule for negative exponents:** $$a^{-n} = \frac{1}{a^n}$$ where $a \neq 0$ and $n$ is a posit

1. The problem is to simplify the expression $$\frac{y^{-6}}{y}$$. 2. Recall the rule for dividing powers with the same base: $$\frac{a^m}{a^n} = a^{m-n}$$.

1. **State the problem:** Simplify the expression $$\frac{y^{-6}}{y}$$. 2. **Recall the rule for dividing powers with the same base:** When dividing powers with the same base, subt

1. **State the problem:** Simplify the expression $$\frac{1}{p^{-1}}$$ and write the result using positive exponents. 2. **Recall the rule for negative exponents:** For any nonzero

1. We are asked to simplify the expression $$\left(-\frac{1}{4}\right)^{-3}$$. 2. Recall the rule for negative exponents: $$a^{-n} = \frac{1}{a^n}$$ where $a \neq 0$.

1. **State the problem:** Solve the system of equations: $$xy=4$$

1. **State the problem:** Solve the equation $$-7 + 7x - 3x = 37$$ for $$x$$. 2. **Combine like terms:** The terms with $$x$$ are $$7x$$ and $$-3x$$. Combine them:

1. The problem is to show that 180000 is greater than another number, which we will call $x$. 2. The inequality to prove is:

1. **State the problem:** Solve the system of equations: $$xy=4$$

1. The problem is to solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. We start by multiplying both sides of the equation by the denominator $x-3$ to eliminate the fraction:

1. The problem is to solve for $x$ in the equation $2x + 3 = 7$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. The problem is to solve for $x$ in the equation $2x + 3 = 7$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. **State the problem:** Solve the quadratic equation $$x^2 + 6x - 2 = 0$$. 2. **Formula used:** The quadratic formula to solve $$ax^2 + bx + c = 0$$ is

1. **State the problem:** Simplify the expression $0.5(b+7)-0.3b+4$. 2. **Apply the distributive property:** Multiply $0.5$ by each term inside the parentheses.

1. **State the problem:** Simplify the expression $(x-9)-(4-2x)$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign to the second group:

1. **State the problem:** Simplify the expression \(\frac{7x + 19}{2x - 7} + 5x + 12\). 2. **Rewrite the problem:** We want to add the rational expression \(\frac{7x + 19}{2x - 7}\

1. The problem asks to write the fraction $-\frac{3}{7}$ as a decimal, using bar notation if necessary. 2. To convert a fraction to a decimal, divide the numerator by the denominat

1. The problem asks: "Golden Gate Park is about ___ % larger than Central Park." We need to find the percentage increase from Central Park's area to Golden Gate Park's area. 2. The

1. **State the problem:** Simplify the expression $\left(\frac{1}{2}x - 3\right) + \left(\frac{1}{6}x + 1\right)$. 2. **Write the expression:**

1. The problem asks to convert the improper fraction $\frac{15}{2}$ into a mixed number. 2. A mixed number consists of a whole number and a proper fraction.

1. The problem involves multiplying the fractions $\frac{19}{6}$ and $\frac{2}{15}$, finding the GCF, and converting $\frac{5}{2}$ to a mixed number. 2. To multiply fractions, mult