Mathematics Grade 10 15 min

Properties of exponents

Properties of exponents

What you'll learn

  • Identify the place value of each digit in numbers up to the billions place with 80% accuracy.
  • Compare two numbers up to the billions place using symbols (>,
  • Explain the process of comparing two large numbers (up to billions) in their own words, including the importance of place value, with a rubric score of at least 3 out of 4.
  • Order a set of three or more numbers up to the billions place from least to greatest or greatest to least correctly in 3 out of 4 attempts.

Tutorial Preview

1

Introduction & Learning Objectives

Learning Objectives Simplify expressions by applying the product and quotient of powers properties. Simplify expressions using the power of a power, power of a product, and power of a quotient properties. Correctly interpret and apply the rules for zero and negative exponents. Simplify complex algebraic expressions that require combining multiple exponent properties. Evaluate numerical expressions involving integer exponents. Apply the properties of exponents to solve problems involving scientific notation. How can we describe the distance to the nearest star, over 40,000,000,000,000 km away, without writing all those zeros? 🔭 Exponents are a powerful shorthand for repeated multiplication. Mastering their properties is a foundational skill in algebra, allowing you to simpl...
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Key Concepts & Vocabulary

TermDefinitionExample BaseThe number or variable that is being multiplied by itself.In the expression 5³, the base is 5. Exponent (or Power)A number that indicates how many times the base is used as a factor in a multiplication.In the expression 5³, the exponent is 3. This means 5 * 5 * 5. PowerThe entire expression consisting of a base and an exponent.The expression 5³ is a power. Zero ExponentAny non-zero base raised to the power of zero is equal to 1.x⁰ = 1 (for x ≠ 0), and 1,257⁰ = 1. Negative ExponentAn exponent that indicates the reciprocal of the base raised to the corresponding positive exponent.x⁻ⁿ = 1/xⁿ. For instance, 3⁻² = 1/3² = 1/9.
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Core Formulas

Product of Powers xᵃ * xᵇ = xᵃ⁺ᵇ When multiplying powers with the same base, keep the base and add the exponents. Quotient of Powers xᵃ / xᵇ = xᵃ⁻ᵇ When dividing powers with the same base, keep the base and subtract the exponents (numerator exponent minus denominator exponent). Power of a Power (xᵃ)ᵇ = xᵃ*ᵇ When raising a power to another power, keep the base and multiply the exponents. Power of a Product & Quotient (xy)ᵃ = xᵃyᵃ and (x/y)ᵃ = xᵃ/yᵃ When a product or quotient is raised to a power, distribute the power to each factor in the base.

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Sample Practice Questions

Challenging
Simplify the expression (3a⁻²b⁰c⁵)⁻². This is similar to a worked example in the tutorial.
A.-9a⁴c¹⁰
B.a⁴ / (9c¹⁰)
C.9a⁴c¹⁰
D.a⁴ / (6c¹⁰)
Challenging
If (xᵃ * x⁻⁴) / x³ = x⁹, what is the value of 'a'?
A.16
B.8
C.2
D.10
Challenging
Which expression is equivalent to (x⁻¹ + y⁻¹)⁻¹?
A.x + y
B.1/(x+y)
C.x²y² / (x+y)
D.xy / (x+y)

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Frequently asked questions

What grade level is "Properties of exponents"?

Properties of exponents is a Grade 10 Mathematics lesson on ExcelOS.

What will I learn in Properties of exponents?

You'll be able to: Identify the place value of each digit in numbers up to the billions place with 80% accuracy; Compare two numbers up to the billions place using symbols (>,; Explain the process of comparing two large numbers (up to billions) in….

Is "Properties of exponents" free to practice?

Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.

How many practice questions are included with Properties of exponents?

This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.

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