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Master Combining Exponents: Rules, Tips, and Examples

Grade 10 Math: Master Essential Skills & Concepts

WA10.1

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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

WA10.10

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

Applications of polynomials

Common factors of polynomials

WA10.11

Solving polynomial equations

Word problems of polynomials

Factoring polynomials by grouping

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

WA10.2

Upper and lower bound

Upper and Lower Bound

WA10.3

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

WA10.4

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

Rational vs. Irrational numbers

WA10.5

Evaluating and simplifying radicals

Converting repeating decimals to fractions

Square and square roots

Square Root of a Perfect Square

Cubic and cube roots

Cube root of a perfect cube

Converting radicals to mixed radicals

WA10.6

Product rule of exponents

Converting radicals to entire radicals

Adding and subtracting radicals

Adding radicals

Subtracting radicals

Multiplying and dividing radicals

Dividing radicals

Multiplying radicals

Rationalize the denominator

WA10.7

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

Solving for exponents

WA10.8

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

What is a polynomial?

Classifying Polynomials

WA10.9

Polynomial components

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

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Workplace and Apprenticeship Mathematics 10

Number Sense, Logical Thinking, Mathematics as a Human Endeavour

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.