Simplify each expression. See Example 1. (½ mn) (8m²n²)

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Identify the expression to simplify: \((\frac{1}{2} mn)(8m^{2}n^{2})\).

Apply the associative property of multiplication to group the coefficients and variables separately: \((\frac{1}{2} \times 8) \times (m \times m^{2}) \times (n \times n^{2})\).

Multiply the numerical coefficients: \(\frac{1}{2} \times 8\).

Use the laws of exponents to combine like bases: \(m^{1} \times m^{2} = m^{1+2} = m^{3}\) and \(n^{1} \times n^{2} = n^{1+2} = n^{3}\).

Write the simplified expression by combining the results from the previous steps: (result of coefficient multiplication) \(m^{3} n^{3}\).

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Multiplication of Algebraic Expressions

This involves multiplying coefficients (numerical parts) and variables separately. When multiplying variables with exponents, you add the exponents if the bases are the same. For example, m × m² = m³.

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Simplifying Trig Expressions

Properties of Exponents

When multiplying powers with the same base, add their exponents: a^m × a^n = a^(m+n). This rule helps simplify expressions like m × m² into m³, making it easier to combine terms.

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Imaginary Roots with the Square Root Property

Simplifying Numerical Coefficients

Multiply the numerical coefficients separately from the variables. For example, (1/2) × 8 = 4. Simplifying coefficients first helps reduce the expression before combining variable terms.

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Domanda del libro di testo

Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. (r⁸/s²)³

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Domanda del libro di testo

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

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