Examples of simplifying expressions with negative and zero exponents.

📚 Quick Study Guide

• 🔢 Zero Exponent Rule: Any non-zero number raised to the power of zero is equal to 1. Mathematically, $a^0 = 1$ (where $a \neq 0$).
• ➖ Negative Exponent Rule: A number raised to a negative exponent is equal to the reciprocal of that number raised to the positive exponent. Mathematically, $a^{-n} = \frac{1}{a^n}$ (where $a \neq 0$).
• ➗ Quotient Rule: When dividing expressions with the same base, subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$. This rule is useful when simplifying expressions with negative exponents in the denominator.
• 💡 Simplifying Strategy: Convert all negative exponents to positive exponents first, then simplify using other exponent rules.

Practice Quiz

1. What is the simplified form of $5^0$?

   1. A) 0
   2. B) 1
   3. C) 5
   4. D) -1

2. What is the simplified form of $3^{-2}$?

   1. A) -9
   2. B) $\frac{1}{9}$
   3. C) 9
   4. D) -6

3. Simplify: $x^{-3}$

   1. A) -x³
   2. B) $\frac{1}{x^3}$
   3. C) x³
   4. D) $\frac{1}{-x^3}$

4. Simplify: $(2y)^{-1}$

   1. A) -2y
   2. B) $\frac{1}{2y}$
   3. C) 2y
   4. D) $\frac{1}{-2y}$

5. Simplify: $\frac{4a^0}{2}$

   1. A) 0
   2. B) 2
   3. C) 4
   4. D) 1

6. Simplify: $\frac{x^{-2}}{x^{-5}}$

   1. A) $x^{-7}$
   2. B) $x^{3}$
   3. C) $\frac{1}{x^3}$
   4. D) $x^{-10}$

7. Simplify: $(a^{-2}b^3)^0$

   1. A) 0
   2. B) 1
   3. C) $a^{-2}b^3$
   4. D) $a^2b^{-3}$