Simplify each expression. See Example 1. (n⁶)(n⁴)(n)

Verified step by step guidance

1. Identify the base and the exponents in the expression \((n^6)(n^4)(n)\). Here, the base is \(n\) for all terms.
2. Recall the exponent rule for multiplying powers with the same base: \(a^m \cdot a^n = a^{m+n}\). This means you add the exponents when multiplying.
3. Apply the rule by adding the exponents of each term: \$6 + 4 + 1\( (note that \)n\( is the same as \)n^1$).
4. Write the simplified expression as \(n^{6+4+1}\).
5. Combine the exponents to express the final simplified form as \(n^{11}\).

Key Concepts

Laws of Exponents

The laws of exponents provide rules for simplifying expressions involving powers. Specifically, when multiplying terms with the same base, you add their exponents. For example, (n^a)(n^b) = n^(a+b). This rule is essential for simplifying expressions like (n^6)(n^4)(n).

Base Consistency in Exponentiation

When applying exponent rules, the base must be the same for the rules to apply directly. In the expression (n^6)(n^4)(n), all terms have the base 'n', allowing the exponents to be combined. Recognizing the base ensures correct application of exponent laws.

Simplification of Algebraic Expressions

Simplification involves rewriting expressions in a simpler or more compact form without changing their value. Using exponent rules to combine powers is a common simplification technique in algebra, making expressions easier to work with or interpret.