🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{p^{-8}}{t^{-2}q^{-9}}$$ and write the answer using only positive exponents. 2. **Recall the exponent rules:**

1. **State the problem:** Simplify the expression $$\frac{10^0 r^{-11} s}{3^2}$$ and write the answer using only positive exponents. 2. **Recall important rules:**

1. **State the problem:** Simplify the expression $$\frac{2^{-2}m^{-3}}{n^{0}}$$ and write the answer using only positive exponents. 2. **Recall important rules:**

1. **State the problem:** Simplify the expression $x^{-7}$ so that it contains only positive exponents. 2. **Recall the rule for negative exponents:** For any nonzero number $a$ an

1. We start with problem 3(a): Evaluate $-\frac{4}{3} \div \frac{2}{-3}$. 2. Division of fractions means multiplying by the reciprocal: $$-\frac{4}{3} \div \frac{2}{-3} = -\frac{4}

1. **State the problem:** We need to show that the roots of the equation $$x^2 - 3x + 2 - c^2 = 0$$ are real.

1. **State the problem:** We need to determine if the product of two rational numbers is always rational. 2. **Recall the definition of rational numbers:** A rational number is any

1. **Classify each number as rational or irrational:** 1. $5 \frac{1}{25}$

1. **State the problem:** Determine if the relation $$y = \frac{3x - 1}{x + 2}$$ is a function. 2. **Recall the definition of a function:** A function assigns exactly one output $$

1. **State the problem:** We need to solve the equation $$\sqrt{x} = 25$$ for $$x$$. 2. **Recall the formula and rule:** The square root function $$\sqrt{x}$$ is the inverse of squ

1. **State the problem:** We need to solve the equation $$\sqrt{x} = 11$$ for $x$.\n\n2. **Recall the formula and rule:** The square root function $\sqrt{x}$ is the inverse of squa

1. **State the problem:** We need to find the measure of an angle given that it is 12 less than twice its complement. 2. **Define variables:** Let the angle be $x$ degrees.

1. **State the problem:** We need to find the measure of an angle given that the difference between twice its measure and its supplement is 27. 2. **Define variables:** Let the ang

1. We are given the equation $$(-4)(x) = -20$$ and need to find the value of $x$. 2. The formula used here is the multiplication property of equality: if $$a \times b = c$$, then $

1. We are given the equation $5 - ( ) = 14$ and need to find the missing number inside the parentheses. 2. Let the missing number be $x$. Then the equation becomes:

1. **State the problem:** We need to determine the order of operations for the expression $$a + \frac{b - c \times d}{f}$$ and identify which operation should be done first. 2. **R

1. **State the problem:** We want to use the linear regression function $$y = 57.14x + 28.57$$ to predict the number of T-shirts sold in the years 2012, 2014, 2016, 2018, and 2020.

1. **State the problem:** We need to find the least common denominator (LCD) of the fractions $\frac{1}{10}$ and $\frac{2}{5}$.\n\n2. **Recall the definition:** The LCD of two frac

1. **State the problem:** We need to find the least common denominator (LCD) of the fractions $\frac{1}{10}$ and $\frac{8}{15}$. 2. **Recall the formula:** The LCD of two fractions

1. **Problemstellung:** Wir sollen die Polynome in Grundform bringen und den Grad $n$ sowie die Koeffizienten $a_k$ angeben. ---

1. **Multiply and simplify:** Problem: Multiply $\frac{4x}{3y^2}$ and $\frac{9y}{8x^3}$ and simplify completely.