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Master Combining Exponents: Rules, Tips, and Examples

Grade 10 Math: Master Essential Skills & Concepts

1.1 Solving Problems Involving Similar Triangles

Similar triangles

Similar polygons

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

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Combining the exponent rules

Isosceles and equilateral triangles

2.1 Solving Problems Involving the Trigonometry of Right Triangles

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

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)

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

3.1 Solving Problems Involving Surface Area and Volume, Using the Imperial and Metric Systems of Measurement

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

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

1.1 Manipulating and Solving Algebraic Equations

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

Introduction to linear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

2.1 Graphing and Writing Equations of Lines

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>

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

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

3.1 Solving and Interpreting Systems of Linear Equations

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Applications of linear equations

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

1.1 Manipulating Quadratic Expressions

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

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

2.1 Identifying Characteristics of Quadratic Relations

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

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

3.1 Solving Problems by Interpreting Graphs of Quadratic Relations

Applications of quadratic functions

Applications of quadratic equations

Get better math marks with our complete Grade 10 math help &ndash; be it <a href="http://www.edu.gov.on.ca/eng/curriculum/secondary/grades.html">Ontario math curriculum</a>, math curricula of <a href="https://curriculum.gov.bc.ca/curriculum/10-12#m">B.C.</a>, <a href="https://education.alberta.ca/mathematics-10-12/programs-of-study/">Alberta</a>, <a href="http://www.edu.gov.mb.ca/k12/cur/math/index.html">Manitoba</a>, <a href="https://www.curriculum.gov.sk.ca/webapps/moe-curriculum-BBLEARN/index.jsp?lang=en&subj=mathematics&level=foundations10">Saskatchewan</a>, <a href="http://www.ed.gov.nl.ca/edu/k12/curriculum/guides/mathematics/">Newfoundland</a>, or other provinces. We&apos;ve got you all covered!

Just like your class or textbook, our complete help for grade 10 math includes topics such as Trigonometry, Quadratic Equations, Radicals, Factoring polynomials, Linear equations, Linear systems, and more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest grade 10 math problems. Then, strengthen your understanding with tons of grade 10 math practice. 

All our lessons are taught by experienced grade 10 math teachers. Let&apos;s finish your homework in no time, and ACE that final.

Foundations of Mathematics, Grade 10, Applied (MFM2P) 

1. Measurement and Trigonometry

2. Modelling Linear Relations

3. Quadratic Relations of the Form y = ax^2 + bx + c

math

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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.