Simplifying Exponential Expressions Guide

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📚 Key Rules & Examples

Product Rule: x^a · x^b = x^(a+b)

Example: 3^4 · 3^2 = 3^(4+2) = 3^6

Quotient Rule: x^a ÷ x^b = x^(a-b)

Example: 5^7 ÷ 5^3 = 5^(7-3) = 5^4

Power Rule: (x^a)^b = x^(a·b)

Example: (2^3)^4 = 2^(3·4) = 2^12

Zero Exponent Rule: x^0 = 1 (where x ≠ 0)

Example: 7^0 = 1

Negative Exponent Rule: x^(-a) = 1/x^a

Example: 4^(-2) = 1/4^2 = 1/16

1. Simplify: 2^5 · 2^3

2. Simplify: x^8 ÷ x^3

3. Simplify: (3^2)^4

4. What is the value of 9^0?

Undefined

5. Simplify: 5^(-3)

6. Which expressions are equivalent to x^6? (Check all that apply)

x^2 · x^4

(x^3)^2

x^8 ÷ x^2

x^3 + x^3

7. Simplify completely: (2^3 · 2^4) ÷ 2^5

8. Simplify: (x^2)^3 · x^(-4)

9. If 3^a = 27 and 3^b = 9, what is the value of 3^(a-b)?

10. Explain in your own words why any number (except zero) raised to the power of 0 equals 1.