Simplify each expression. (n6)(n4)(n)

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 13

1장, 문제 13

Simplify each expression. (n⁶)(n⁴)(n)

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Identify the base and the exponents in the expression \((n^{6})(n^{4})(n)\). Here, the base is \(n\) for all terms.

Recall the product of powers property: when multiplying expressions with the same base, add their exponents. That is, \(a^{m} \times a^{n} = a^{m+n}\).

Apply this property to the given expression by adding the exponents: \(6 + 4 + 1\) (note that \(n\) is the same as \(n^{1}\)).

Write the simplified expression as \(n^{6+4+1}\).

Combine the exponents by performing the addition inside the exponent to get the final simplified form \(n^{11}\) (do not calculate the final value, just show the step).

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Laws of Exponents

The laws of exponents provide rules for simplifying expressions involving powers of the same base. For multiplication, the exponents are added together, such as a^m * a^n = a^(m+n). This rule is essential for combining terms like n^6, n^4, and n^1.

Base Consistency in Exponents

When multiplying exponential expressions, the bases must be the same to apply the exponent addition rule. In the given expression, all terms have the base 'n', allowing the exponents to be combined directly.

Simplification of Algebraic Expressions

Simplification involves rewriting expressions in a more compact or standard form. By applying exponent rules correctly, the product of powers can be expressed as a single term with one exponent, making the expression easier to understand and use.