Mathematics
Grade 9
15 min
Powers of monomials
Powers of monomials
What you'll learn
- Identify the base and exponent in a monomial expression raised to a power with 80% accuracy on a worksheet.
- Apply the power of a power rule to simplify monomial expressions with at least 75% accuracy on a quiz.
- Solve problems involving powers of monomials, including those with coefficients and multiple variables, achieving a score of 70% or higher on a problem set.
- Explain in writing how the power of a product rule is used when simplifying powers of monomials, demonstrating understanding in a short paragraph of at least 5 sentences.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define a monomial and identify its components (coefficient, variable, exponent).
Apply the Power of a Power rule to simplify monomials raised to a power.
Apply the Power of a Product rule to simplify products raised to a power.
Simplify complex monomial expressions involving multiple variables and negative coefficients.
Evaluate a monomial raised to a power for given variable values.
Apply the concept of powers of monomials to solve problems involving geometric formulas for area and volume.
Ever wondered how the volume of a cube changes if you double its side length? 🧊 It's not double the volume—it's all about the power of monomials!
This tutorial will teach you how to raise a monomial—a simple algebraic term—to a power. You'll learn the...
2
Key Concepts & Vocabulary
TermDefinitionExample
MonomialA monomial is an algebraic expression consisting of a single term, which can be a number, a variable, or a product of a number and one or more variables with non-negative integer exponents.5x^2y is a monomial. 5 is the coefficient, and x and y are the variables.
CoefficientThe numerical factor of a term.In the monomial -8a^3, the coefficient is -8.
BaseThe number or variable that is being raised to a power (multiplied by itself).In the expression y^4, the base is y.
ExponentA number indicating how many times to multiply the base by itself.In the expression y^4, the exponent is 4. This means y * y * y * y.
PowerAn expression that represents repeated multiplication of the same factor. It consists of a base and an exponent.(2x)^3 is a power, where 2x is the base...
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Core Formulas
Power of a Power Rule
(x^a)^b = x^{a \cdot b}
To raise a power to another power, you keep the base and multiply the exponents. This is the core rule for handling exponents on variables.
Power of a Product Rule
(xy)^a = x^a y^a
To find the power of a product, you raise each factor inside the parentheses to that power. This rule allows you to distribute the outer exponent to the coefficient and each variable.
Power of a Monomial (Combined Rule)
(cx^a y^b)^n = c^n x^{a \cdot n} y^{b \cdot n}
This rule combines the others. To raise an entire monomial to a power, raise the coefficient to that power, and for each variable, multiply its exponent by the outer power.
5 more steps in this tutorial
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Challenging
Simplify the nested expression `((2k^3)^2)^3`.
A.64k^{18}
B.12k^{18}
C.64k^8
D.8k^{18}
Challenging
The side length of a cube is `3a^2`. If the side length is doubled to `6a^2`, by what factor does the volume increase?
A.2
B.4
C.6
D.8
Challenging
Find the value of `n` that makes the equation `(x^{n} ⋅ x^3)^2 = x^{18}` true.
A.3
B.15
C.6
D.9
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Frequently asked questions
What grade level is "Powers of monomials"?
Powers of monomials is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Powers of monomials?
You'll be able to: Identify the base and exponent in a monomial expression raised to a power with 80% accuracy on a worksheet; Apply the power of a power rule to simplify monomial expressions with at least 75% accuracy on a quiz; Solve problems….
Is "Powers of monomials" 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 Powers of monomials?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.