Power Properties Rules and Examples

1. 6-1 & 6-2 Properties of Powers Product of Powers: Power of a Power: Power of a Product: Rule: When you multiply with the same base, you ADD the exponents Rule: When raise a power to a power, you MULTIPLY the exponents Rule: When you raise a product to a power, you apply the power to ALL parts of the product

2. 6-1 & 6-2 Properties of Powers Quotient of Powers: Power of a Quotient: Zero Exponent: Rule: When you divide with the same base, you SUBTRACT the exponents Rule: When you raise a quotient to a power, you apply the power to both numerator AND denominator Rule: Anything raised to the zeroth power equals 1

3. 6-1 & 6-2 Negative Exponents Negative Exponents: Rule: When you raise to a negative power, you reciprocate the base, and raise it to the positive power.

4. 6-1 & 6-2 Perfect Squares up to 15 12 = 1 62 = 36 112 = 121 22 = 4 72 = 49 122 = 144 32 = 9 82 = 64 132 = 169 42 = 16 92 = 81 142 = 196 52 = 25 102 = 100 152 = 225

5. 6-1 & 6-2 Perfect Cubes • 13 = 1 63 = 216 • 23 = 8 73 = 343 • 33 = 27 • 43 = 64 • 53 = 125

6. 6-1 & 6-2 Perfect “Quarts” • 14 = 1 • 24 = 16 • 34 = 81 • 44 = 256 • 54 = 625

7. 6-1 & 6-2 Perfect “Quints” • 15 = 1 • 25 = 32 • 35 = 243

8. 6-1 & 6-2 Rational Exponents

9. 6-1 & 6-2 Number of Real Roots Every positive real number has: 2 real nth roots, when n is even 1 real nth root, when n is odd Every negative real number has: 0 real nth roots, when n is even 1 real nth root, when n is odd

10. 6-1 & 6-2 Negative Rational Exponents A negative rational exponent can be split into 3 parts: reciprocal power root