Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3.-(4m³n⁰)²

Verified step by step guidance

1. Identify the expression to simplify: \(-(4m^3n^0)^2\).
2. Recall that any number raised to the power of zero is 1, so \(n^0 = 1\).
3. Simplify the expression inside the parentheses: \(4m^3 \cdot 1 = 4m^3\).
4. Apply the power of a power property: \((4m^3)^2 = 4^2 \cdot (m^3)^2\).
5. Simplify further: \(-(4^2 \cdot m^{3 \times 2}) = -(16m^6)\).

Key Concepts

Exponent Rules

Exponent rules are fundamental principles that govern how to manipulate powers of numbers and variables. Key rules include the product of powers (a^m * a^n = a^(m+n)), the power of a power ( (a^m)^n = a^(m*n) ), and the power of a product ( (ab)^n = a^n * b^n ). Understanding these rules is essential for simplifying expressions involving exponents.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the opposite positive exponent. For example, a^(-n) = 1/(a^n). This concept is crucial when simplifying expressions that involve negative powers, as it allows for the transformation of the expression into a more manageable form.

Polynomial Simplification

Polynomial simplification involves combining like terms and applying exponent rules to reduce expressions to their simplest form. This process often includes distributing coefficients and managing variables with exponents, which is vital for accurately simplifying algebraic expressions, especially those involving multiple variables.