🧮 algebra

1. **State the problem**: Simplify the expression $$\frac{\sqrt{125a^2b}^{-3}}{5ab^{-1}}.$$\n\n2. **Rewrite the expression**: The numerator is $\left(\sqrt{125a^2b}\right)^{-3}$ an

1. The problem is to explain what a linear equation is. 2. A linear equation is an algebraic equation of the form $ax + b = 0$, where $a$ and $b$ are constants and $x$ is the varia

1. The user request is unclear and does not present a specific algebra problem to solve. 2. Without a concrete algebraic expression or question, we cannot perform algebraic manipul

1. The problem is to find the value of $16^{0.25}$. 2. Recall that raising a number to the power 0.25 is the same as taking the fourth root of that number because $0.25 = \frac{1}{

1. The given expression is a fraction: $\frac{-16}{24}$. 2. To simplify this fraction, find the greatest common divisor (GCD) of 16 and 24.

1. State the problem: Find the smallest prime number $x$ such that $3 - 4x < -41$. 2. Solve the inequality:

1. Muammoni bayon qilamiz: $$\sqrt{2} - 2 - \sqrt{1} - 4\sqrt{9} - \sqrt{80}$$ ifodasining qiymatini topish. 2. Har bir ildiz ifodalarini hisoblaymiz:

1. **State the problem:** A manager plans to produce 100 bicycles with 25 persons working $d$ hours daily.

1. The "arrow method" typically refers to solving linear equations or systems by using visual steps or arrow diagrams to show the flow of operations. 2. Since no specific equation

1. **State the problem:** Factorize the expression $$x^2 - 36y^2 + 2x^3 y^2 - 12 x^2 y^3$$. 2. **Rewrite the expression:** Group terms for easier factorization:

1. The problem is to solve an equation using the inverse method or the direct method. 2. Let's suppose the equation is $ax = b$ where $a$ and $b$ are known constants and $x$ is the

1. **State the problem:** A manager plans to produce 100 bicycles using 25 persons working some hours daily. We need to find how many bicycles can be produced by 40 persons working

1. Stating the problem: Factorize the quadratic expression $$-3x^2 + 7x + 6$$. 2. First, factor out the negative sign for easier manipulation: $$-3x^2 + 7x + 6 = -(3x^2 - 7x - 6)$$

1. Stating the problem: Simplify and factor the expression $$-3(1-2y)^2 + 7(1-2y) + 6$$. 2. Expand the squared term: $$(1-2y)^2 = 1 - 4y + 4y^2$$.

1. **State the problem:** Simplify the expression $$\frac{27.5 \times 10^{-3}}{28} \Big/ \left( \frac{27.5 \times 10^{-3}}{28} + \frac{180}{18} \right)$$. 2. **Rewrite the expressi

1. **State the problem:** We have a set of 7 consecutive odd numbers. 2. Let the smallest odd number be $x$. Then the numbers are: $x, x+2, x+4, x+6, x+8, x+10, x+12$.

1. The problem is to simplify the expression $$\frac{48 \times 18}{(18 \times 46) + (36 \times 92)}$$. 2. First, calculate the numerator: $$48 \times 18 = 864$$.

1. **State the problem:** Simplify the expression $$(2a^6 - 6a^3)^2$$. 2. **Recognize the form:** This is a square of a binomial, so we use the formula $$(x - y)^2 = x^2 - 2xy + y^

1. Stating the problem: Simplify the expression $$(4+3c^5)(4-3c^5)(4+3c^5)(4-3c^5)(4+3c^5)(4-3c^5)$$. 2. Notice the expression is of the form $$(a+b)(a-b)(a+b)(a-b)(a+b)(a-b)$$ whi

1. Stating the problem: We want to simplify the expression $(4+3c^5)(4-3c^5)$.\n\n2. This expression is in the form of $(a+b)(a-b)$, which is a difference of squares formula: $$ (a

1. The problem is to expand the expression $$(4+7a^2)^2$$. 2. Use the formula for the square of a binomial: $$(x+y)^2 = x^2 + 2xy + y^2$$ where here $x=4$ and $y=7a^2$.