Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. 6^4/6^-2

Verified step by step guidance

1. Identify the expression: \( \frac{6^4}{6^{-2}} \).
2. Apply the property of exponents: \( \frac{a^m}{a^n} = a^{m-n} \).
3. Subtract the exponents: \( 6^{4 - (-2)} \).
4. Simplify the exponent: \( 6^{4 + 2} \).
5. Rewrite the expression with the simplified exponent: \( 6^6 \).

Key Concepts

Exponents and Their Properties

Exponents represent repeated multiplication of a base number. Key properties include the product of powers (a^m * a^n = a^(m+n)), the quotient of powers (a^m / a^n = a^(m-n)), and the power of a power ( (a^m)^n = a^(m*n)). Understanding these properties 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 to ensure that all terms are expressed without negative exponents, as specified in the problem.

Simplification of Algebraic Expressions

Simplifying algebraic expressions involves reducing them to their simplest form by combining like terms and applying exponent rules. This process often includes eliminating negative exponents and ensuring that the expression is presented in a clear and concise manner, which is the goal of the given problem.