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Rational Exponents

You solutions may follow different paths than mine but still be correct.

Questions

1. Write down the rules of exponents.
2. Simplify
3. Simplify

4. Simplify so there are no negative exponents.
5. Simplify so there are no negative exponents.
6. Simplify
7. Simplify
8. Simplify
9. Simplify

10. Factor out the common factor 2a in
11. Factor out the common factor 2a in
12. Factor out the common factor 3x in

Solutions

1. The rules of exponents are:

• x⁰ = 1 if x ≠ 0 (0⁰ is indeterminant and is dealt with in calculus).
• Product Rule:
• Quotient Rule:
• Power Rule:
• Product Raised to Power Rule:
• Quotient Raised to a Power Rule:
• Negative Exponent: , if x ≠ 0.

2. Using Power Rule
Simplify, using Power Rule and Negative Exponent Rule
Simplify, using Negative Exponent Rule
Simplify, using Product Rule
Simplify