🧮 algebra

1. **State the problem:** We need to subtract the polynomial \( (5k^2 - 3) \) from \( (-2k + 4k^2 + 6) \). 2. **Write the expression:**

1. **State the problem:** Simplify the expression $$\frac{v^2 - 3v + 2}{v^2 - 1}$$ and find its simplified form. 2. **Recall the formula and rules:** To simplify a rational express

1. **State the problem:** Find all excluded values for the expression $$\frac{x + 8}{x^2 - 3x - 18}$$ which are values of $x$ that make the denominator zero. 2. **Recall the rule:*

1. The problem is to rearrange the formula $F = ma$ to solve for $m$. 2. The formula given is $F = ma$, where $F$ is force, $m$ is mass, and $a$ is acceleration.

1. **State the problem:** Simplify the expression \(\sqrt[6]{\sqrt{15}}\). 2. **Rewrite the expression using exponents:** The square root of 15 is \(15^{\frac{1}{2}}\), so the expr

1. **State the problem:** Simplify the expression $$\frac{\sqrt{27}}{\sqrt{12}}$$. 2. **Use the property of square roots:** $$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$$.

1. **State the problem:** Simplify the expression $\sqrt{3a} \times \sqrt{6a}$.\n\n2. **Recall the property of square roots:** The product of square roots is the square root of the

1. The problem is to simplify the expression $-27^{1/3}$. 2. The expression involves a negative sign and a cube root. The cube root of a number $a$ is written as $a^{1/3}$.

1. The problem is to simplify the expression $-25^{1/2}$. 2. The exponent $1/2$ means the square root, so $25^{1/2} = \sqrt{25}$.

1. **State the problem:** Simplify the expression $(64n^6)^{\frac{1}{3}}$. 2. **Recall the rule:** When raising a power to a fractional exponent, use the rule $a^{\frac{m}{n}} = \s

1. **State the problem:** Simplify the expression $$(64n^3)^{\frac{1}{3}}$$. 2. **Recall the rule:** When raising a power to a fractional exponent, use the rule $$a^{\frac{m}{n}} =

1. **Problem statement:** Given the function $$f_r(x) = \frac{x^2 - 4}{|x| - 1}$$ defined on its domain, determine which of the points A(0,2), B(-2,0), C(1,0), and D(0,4) belong to

1. The problem asks if the statement $-3^{-4} = \frac{1}{81}$ is true or false. 2. Recall the order of operations: exponents are evaluated before negation.

1. The problem asks if $-8^{3/4}$ equals the 4th root of $-8^3$. 2. Recall the exponent rule: $a^{m/n} = \sqrt[n]{a^m}$.

1. The problem asks whether the 5th root of 32 equals 2. 2. The 5th root of a number $a$ is a number $b$ such that $b^5 = a$.

1. **State the problem:** Determine if the equation $$\sqrt[18]{5} = \sqrt[6]{5} \times \sqrt[3]{5}$$ is true or false. 2. **Recall the rule for roots:** The $n$th root of a number

1. The problem states the property of radicals: For any real number $n$, the $n$th root of $a^m$ is equal to $a^{m/n}$. 2. The formula used is:

1. The problem asks whether for any real number $n$, the equation $$\sqrt[n]{ab} = \sqrt[n]{a} \times \sqrt[n]{b}$$ is true. 2. The formula used here is the property of radicals: $

1. **State the problem:** We need to determine if the statement "If $n$ is even and $a$ is negative, then the $n$th root of $a$ is not a real number" is true or false. 2. **Recall

1. **State the problem:** Determine if the set $A = \{ f_{a,b} : a,b \in \mathbb{R} \}$ with the operation of composition $(A, \circ)$ forms a monoid, and whether $(A, \circ)$ is a

1. The problem asks whether the statement "An exponent determines how many times the base is multiplied to itself" is true or false. 2. Recall the definition of an exponent: For a