Category: Algebra

Exo 1 Simplify the following expressions with positive exponents. \((5x^{-7}y^3)^{-5}\) Solution: Step 1: Apply the exponent to each term inside the parentheses Use the property \( (ab)^n = a^n \cdot b^n \) to distribute the exponent \(-5\) to each factor: \[ (5x^{-7}y^3)^{-5} = 5^{-5} \cdot (x^{-7})^{-5} \cdot (y^3)^{-5} \] Step 2: Simplify each term \( […]

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1. Basic Arithmetic Formulas Addition and Subtraction: \( a + b = b + a \) (Commutative property) Multiplication and Division: \( a \times b = b \times a \) (Commutative property) \( \frac{a}{b} \) (Quotient) 2. Exponents and Powers Power of a product: \[ (ab)^n = a^n \times b^n \] Power of a quotient: […]

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Find the total number of pages in the book: Marie has finished \( \frac{3}{4} \) of a book. She found that she has read 106 more pages than the number of pages left to read. What is the total number of pages in the book? Solution: Let \(x\) be the total number of pages in […]

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Word problem 1: A salesman sold twice as many pears in the afternoon as he did in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon? Solution Let’s break the problem down step by step: Let \( x […]

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Solve for \(x\) where \[ -4|6x + 2| = -16 \] Solution To solve the absolute value equation \(-4|6x + 2| = -16\), follow these steps: Step 1: Divide both sides by \(-4\) We start by isolating the absolute value expression. Divide both sides of the equation by \(-4\): \[ |6x + 2| = 4 […]

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