Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:15 minutes

Problem 16

Textbook Question

Simplify each expression. See Example 1. (4^2)(4^8)

Verified step by step guidance

Identify the expression to simplify: \((4^2)(4^8)\).

Recognize that the expression involves multiplying powers with the same base.

Apply the property of exponents: \(a^m \cdot a^n = a^{m+n}\).

Add the exponents: \(2 + 8\).

Rewrite the expression as a single power of 4: \(4^{2+8}\).

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Key Concepts

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

Exponential Rules

Exponential rules are mathematical principles that govern the operations involving exponents. One key rule is that when multiplying two expressions with the same base, you add their exponents. For example, a^m * a^n = a^(m+n). This rule is essential for simplifying expressions like (4^2)(4^8) by combining the exponents.

Base of an Exponent

The base of an exponent is the number that is raised to a power. In the expression 4^n, 4 is the base, and n is the exponent. Understanding the base is crucial because it determines the value of the expression when combined with the exponent. In the given expression, both terms share the same base of 4, allowing for simplification.

Simplification of Expressions

Simplification of expressions involves reducing a mathematical expression to its simplest form. This process often includes combining like terms, applying arithmetic operations, and using algebraic rules. In the context of the question, simplifying (4^2)(4^8) means applying the exponential rule to express the product as a single exponent, resulting in 4^(2+8) = 4^10.