Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. 6⁴/6^-2

Verified step by step guidance

1. Identify the expression to simplify: \(\frac{6^4}{6^{-2}}\).
2. Recall the property of exponents for division with the same base: \(\frac{a^m}{a^n} = a^{m-n}\).
3. Apply the property to the expression: \$6^{4 - (-2)}$.
4. Simplify the exponent by subtracting the negative exponent: \$4 - (-2) = 4 + 2$.
5. Write the expression with the simplified exponent: \$6^{6}$. This expression has no negative exponents.

Key Concepts

Laws of Exponents

The laws of exponents govern how to simplify expressions involving powers. For example, when dividing like bases, subtract the exponents: a^m / a^n = a^(m-n). This rule is essential for simplifying expressions such as 6^4 / 6^-2.

Negative Exponents

A negative exponent indicates the reciprocal of the base raised to the positive exponent: a^(-n) = 1 / a^n. Understanding this helps rewrite expressions without negative exponents, as required in the problem.

Simplification of Expressions

Simplification involves applying exponent rules to rewrite expressions in their simplest form, often eliminating negative exponents and combining like terms. This process makes expressions easier to interpret and use.