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Master Combining Exponents: Rules, Tips, and Examples

Grade 10 Math: Master Essential Skills & Concepts

Operations on powers with integral exponents

Product rule of exponents

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Exponents: Product rule (a^x)(a^y) = a^(x+y)

Exponents: Division rule: a^x / a^y = a^(x-y)

Exponents: Power rule: (a^x)^y = a^(xy)

Exponents: Power rule

Exponents: Negative exponents

Exponents: Zero exponent: a^0 = 1

Exponents: Rational exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

Solving for exponents

Prime factorization

Evaluating and simplifying radicals

Number properties: Prime or Composite

Number properties: Prime?

Prime factors – Word Problem

Greatest common factors (GCF)

Greatest Common Factor 2 Numbers

Greatest Common Factor 2 Numbers – Word Problem

Least common multiple (LCM)

Lowest Common Multiple - 2 Numbers – Word Problem

Lowest Common Multiple 2 Numbers

Square and square roots

Square Root of a Perfect Square

Cubic and cube roots

Cube root of a perfect cube

Functions and relations: connecting data, graphs, and situations

Introduction to quadratic functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Quadratic function in vertex form: y = a(x-p)^2 + q

Linear functions: slope and equations of lines

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

Point-slope form: y - y_1 = m(x - x_1)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Systems of linear equations

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

Linear programming word problems

Word problems relating 3 variable systems of equations

Solving 3 variable systems of equations (no solution, infinite solutions)

System of Equations With No Solution

System of Equations With Infinite Solutions

System of Equations With Infinite Solutions - Extended

Solving systems of linear equations by graphing

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

Multiplication of polynomial expressions

What is a polynomial?

Classifying Polynomials

Polynomial components

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of polynomials

Polynomial factoring

Factoring polynomials: ax^2 + bx + c

Factoring Polynomials: ax^2 + bx + c

Factoring difference of cubes

Factoring sum of cubes

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Factoring perfect square trinomials

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Find the difference of squares

Evaluating polynomials

Using algebra tiles to factor polynomials

Solving polynomial equations

Word problems of polynomials

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

Common factors of polynomials

Factoring polynomials by grouping

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

Factoring polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

Primary trigonometric ratios

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Combination of SohCahToa questions

Use tangent ratio to calculate angles and sides (Tan = o / a)

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

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Foundations of Mathematics and Pre-Calculus 10

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Ex. 1:

Intro

Understanding why each exponent rule works through expansion

- Hi, welcome to this question here. Well, this one looks a very, very hard question but it's actually not. See, what we have to remember is actually the order of operations which is called the PEMDAS, right? You want to do what's in the brackets first. So, let's not worry about the 3 on the outside first, let's just kind of consider what is happening inside, everything here is multiplying and dividing, we've got an "a" and "b", it's just "a" and "b" with some numbers in the front. So let's deal one thing at a time. So here we go, let's have the bigger brackets on the outside so just to remind ourselves that we're gonna do the power of 3 at the very end. So, I have a negative 16, I've got a 3, I've got a 2. So, that means we will still have a negative. 16 and "a", we're gonna do a quick reduce right there and that's gonna be an 8 right there. And 8 x 3 gives you, 24. So, let's put 24 there and we're done with all the coefficients, then let's do the "a". That's a 5 and that's a 3, these guys are multiplying so you add exponents. So it's 8 so far, and there's a 2 down here, with the same base of "a", 
right? This is all the same base, you can actually just deal with the exponents. So, we've got a 5 plus 3, 8. Subtracted 2, it's 6. So, it's a to the power of 6. Does that make sense? 
Then we've got a "b". Again, they have the same base here and here and here. Negative 3 multiplying, so we've got to do negative 3 plus the 5, which is 2 and then 2 minus negative 2. So, it's gonna give you a 4. I'm gonna get a "b" to the power of 4 right here. And guess what? That's it. That's basically what happens in the inside here. It's just that and we have to raise it to the power of 3. The power of 3 just kind of multiplies to everything. The negative to the power of 3 is still negative. The 24 to the power of 3 is such a big number that we can actually leave it as it is, or you can actually simply punch it in the calculator and you get the answer for that. So, it's 13824 and we can do "a" to the power of 6 to the power of 3 we've got an 18 right there. And then we've got a 4 and 3, and that's that. Hopefully, that's correct. So that's the final answer. Nice and easy, right? Thanks for watching.

Simplifying a complex fraction with multiple exponent rules

Simplifying expressions with variable exponents using product and quotient rules

Simplifying a complex expression with multiple exponent rules

We have now learned all individual exponent rules in the previous sessions. In this session, we will try to use different exponent rules to solve problems.