Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

0. Review of College Algebra

Solving Linear Equations

Trigonometry

0. Review of College Algebra

Solving Linear Equations

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2:04 minutes

Problem 11

Textbook Question

Simplify each expression. See Example 1.(-4x⁵) (4x²)

Verified step by step guidance

Identify the coefficients and the variables in the expression: \((-4x^5)\) and \((4x^2)\).

Multiply the coefficients: \(-4\) and \(4\).

Apply the product of powers property for the variables: \(x^5\) and \(x^2\).

Combine the results from the previous steps: multiply the coefficients and add the exponents of the same base.

Write the simplified expression using the results from the previous steps.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Multiplication of Monomials

Multiplying monomials involves multiplying their coefficients and adding their exponents when the bases are the same. For example, when multiplying (-4x⁵) and (4x²), you multiply -4 and 4 to get -16, and then add the exponents of x (5 + 2 = 7), resulting in -16x⁷.

Exponent Rules

Exponent rules are essential for simplifying expressions involving powers. The key rule for multiplication states that when multiplying like bases, you add the exponents. This rule is crucial for correctly simplifying expressions like (-4x⁵)(4x²) to ensure accurate results.

Combining Like Terms

Combining like terms is the process of simplifying expressions by merging terms that have the same variable raised to the same power. In the context of the given expression, after applying multiplication and exponent rules, understanding how to combine any resulting like terms is vital for achieving the simplest form of the expression.