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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2:08 minutes

Problem 13

Textbook Question

Simplify each expression. See Example 1.n⁶ • n⁴ • n

Verified step by step guidance

Identify the expression to simplify: \( n^6 \cdot n^4 \cdot n \).

Recall the property of exponents: when multiplying like bases, you add the exponents.

Apply the property: \( n^6 \cdot n^4 \cdot n^1 = n^{6+4+1} \).

Simplify the expression by adding the exponents: \( n^{11} \).

The simplified expression is \( n^{11} \).

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Key Concepts

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

Exponent Rules

Exponent rules are fundamental principles that govern the operations involving powers of numbers or variables. Key rules include the product of powers rule, which states that when multiplying like bases, you add the exponents (a^m * a^n = a^(m+n)). Understanding these rules is essential for simplifying expressions involving exponents.

Multiplication of Exponents

When multiplying expressions with the same base, the exponents are combined by addition. For example, in the expression n⁶ • n⁴ • n, the base 'n' is consistent across all terms, allowing us to sum the exponents (6 + 4 + 1) to simplify the expression. This concept is crucial for efficiently handling polynomial expressions.

Simplification of Algebraic Expressions

Simplification involves reducing an expression to its most concise form while maintaining its value. In the context of exponents, this means applying the exponent rules to combine like terms and eliminate unnecessary complexity. Mastery of simplification techniques is vital for solving algebraic problems effectively.