Properties of Exponents

Negative Exponents and Power of a Quotient

Understanding how to simplify expressions with exponents is a fundamental skill in College Algebra. This topic covers the rules for negative exponents and how to apply them to quotients and powers.

• Negative Exponent Rule: For any nonzero number x and integer n, .

• Power of a Quotient Rule: For any nonzero numbers a and b, and integer n, .

• Power of a Power Rule: .

Example: Simplifying the Expression

Given the expression:

• Apply the negative exponent rule:

• Apply the power of a quotient rule:

• Simplify further:

• Final answer:

Key Points

• Negative exponents indicate reciprocals.

• When raising a quotient to a power, raise both numerator and denominator to that power.

• When raising a power to another power, multiply the exponents.

Additional info:

• These rules are foundational for simplifying algebraic expressions and solving equations in College Algebra.