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Master Combining Exponents: Rules, Tips, and Examples

NL.SO.1201AN1

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Understanding the number systems

Prime factorization

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

NL.SO.1201AN2

Evaluating and simplifying radicals

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Converting radicals to mixed radicals

Converting radicals to entire radicals

NL.SO.1201AN3

Product rule of 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

NL.SO.1201AN4

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

NL.SO.1201AN5

Solving polynomials with the unknown 

Solving polynomials with the unknown "b" from ax^2 + bx + c

Factoring polynomials: ax^2 + bx + c

Factoring Polynomials: ax^2 + bx + c

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

Using algebra tiles to factor polynomials

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

NL.SO.1201M1

Upper and lower bound

Upper and Lower Bound

Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Metric systems

Add and Subtract Mixed Units

Metric Length Conversion

Add or Subtract Different Metric Units Convert to CM

Add or Subtract Different Metric Units Convert to M

Add or Subtract Different Metric Units Convert to MM

Imperial systems

Imperial Length Conversion

Conversions involving squares and cubic

Imperial to Metric Conversions — Squares and Cubes

Imperial Conversion — Squares and Cubes

Metric to Imperial Conversion — Squares and Cubes

Metric Area Conversion FT to CM

Metric Area Conversion Foot to Inch

Metric Area Conversion M/CM to Inch

NL.SO.1201M2

Direct variation

Identifying direct variations

NL.SO.1201M3

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

NL.SO.1201M4

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

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

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

NL.SO.1201RF1

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

NL.SO.1201RF2

Identifying functions

Function notation

Function notation (advanced)

NL.SO.1201RF3

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

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

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>

NL.SO.1201RF4

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)

Rate of change

NL.SO.1201RF5

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

NL.SO.1201RF6

Introduction to linear equations

Introduction to nonlinear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

NL.SO.1201RF7

Parallel and perpendicular lines in linear functions

Applications of linear relations

Applications of linear equations

Academic Mathematics 1201

Algebra and Number

Measurement

Relations and Functions

math

Ex. 1:

Intro

<p>- 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",<br />
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?<br />
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.</p>


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.