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

Verified step by step guidance

1. Identify the base and the exponents in the expression \(n^{6} \cdot n^{4} \cdot n\). Here, the base is \(n\) for all terms.
2. Recall the law of exponents for multiplication with the same base: \(a^{m} \cdot a^{n} = a^{m+n}\). This means you add the exponents when multiplying powers with the same base.
3. Apply the exponent addition rule to the expression: \(n^{6} \cdot n^{4} \cdot n^{1} = n^{6+4+1}\).
4. Add the exponents together: \$6 + 4 + 1$ to get the new exponent.
5. Write the simplified expression as \(n^{(6+4+1)}\) or \(n^{11}\) (do not calculate the final exponent value if you want to stop here).

Key Concepts

Laws of Exponents

The laws of exponents govern how to simplify expressions involving powers of the same base. 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 n⁶ • n⁴ • n.

Understanding Base and Exponent

In an expression like n^k, 'n' is the base and 'k' is the exponent, indicating how many times the base is multiplied by itself. Recognizing the base and exponent helps apply exponent rules correctly, especially when combining terms with the same base.

Simplification of Algebraic Expressions

Simplification involves rewriting expressions in a more compact or standard form without changing their value. For expressions with exponents, this means applying exponent rules to combine terms and reduce complexity, making the expression easier to interpret or use in further calculations.