Basics of Algebra Multiplication and Division by Exponents [ begin{align*} &text{Simplify the following expression: } frac{3 x^4}{left(x^{-2}right)^2} \ &(A) quad 3x^{10} \ &(B) quad 3x^{8} \ &(C) quad 3x^{2} \ &(D) quad 3x^{-4} end{align*} ] [ begin{align*} &text{Simplify the following expression: } frac{5 y^{6}}{(y^{-3})^2} \ &(A) quad 5y^{12} \ &(B) quad 5y^{9} \ &(C) quad …
Basics of Algebra Multiplication and Division by Exponents [ begin{align*} &text{Simplify the following expression: } frac{3 x^4}{left(x^{-2}right)^2} \ &(A) quad 3x^{10} \ &(B) quad 3x^{8} \ &(C) quad 3x^{2} \ &(D) quad 3x^{-4} end{align*} ] [ begin{align*} &text{Simplify the following expression: } frac{5 y^{6}}{(y^{-3})^2} \ &(A) quad 5y^{12} \ &(B) quad 5y^{9} \ &(C) quad …
Basics of Algebra 2. The Quadratic Formula (Your Last Resort) All quadratics can be solved using this formula: [ x = frac{{-b pm sqrt{{b^2 – 4ac}}}}{{2a}} ] Let’s solve the quadratic equation below. [ 2x^2 – 5x + 3 = 0 ] [ Rightarrow a = 2, b = -5, c = 3] Substituting the …
Basics of Algebra 1. Basic Factoring [ text{ Solve for } x: ] [ x^2+6x+8 = 0] To solve this quadratic equation by factoring, we can look for two numbers that multiply to give 8 and add up to 6. These numbers are 2 and 4. Therefore, we can rewrite the equation as [(x + …
Basics of Algebra 1. FOIL Method and Distributive Property The FOIL method is used to multiply two binomial expressions, while the distributive property allows us to multiply a constant with a binomial. Let’s demonstrate with an example: [ (2x+1)(3x-2) ] Applying the FOIL method: [ begin{align*} text{First:} & quad 2x cdot 3x = 6x^2 \ …
Basics of Algebra 4. Fractions Addition and Multiplication Addition Rule: To add fractions with different denominators, find a common denominator, add the numerators, and keep the common denominator. [ frac{1}{3} + frac{2}{5} = frac{5}{15} + frac{6}{15} = frac{11}{15} ] Multiplication Rule: To multiply fractions, multiply the numerators together and the denominators together. [ frac{1}{3} times …
Basics of Algebra 1. The 4 Important Exponents Rules Here is a brief introduction to the four important rules for exponents in algebra: Product of Powers Rule: When multiplying two terms with the same base, we add the exponents. Example with numbers: (2^3 cdot 2^4 = 2^{3+4} = 2^7) Example with variables: (x^3 cdot x^4 …
Exponents Rules 1. The 4 Important Exponents Rules Here is a brief introduction to the four important rules for exponents in algebra: Product of Powers Rule: When multiplying two terms with the same base, we add the exponents. Example with numbers: (2^3 cdot 2^4 = 2^{3+4} = 2^7) Example with variables: (x^3 cdot x^4 = …
Sure, here’s how to solve for k: To isolate k, we can square both sides of the equation: Simplifying the left-hand side: Subtracting 5 from both sides: Dividing both sides by 2: Taking the square root of both sides: So the solutions for …
Sure, here’s how to solve for k: $$ \sqrt{2k^2 + 5} = 8 $$ To isolate k, we can square both sides of the equation: $$ (\sqrt{2k^2 + 5})^2 = 8^2 $$ Simplifying the left-hand side: $$ 2k^2 + 5 = 64 $$ Subtracting 5 from both sides: $$ 2k^2 = 59 $$ Dividing both …
