1. Rational Exponents Section 7.4 1/15/2019 12:58 AM

2. DEFINITIONS EXPONENT BASE
Base: The term/variable of which is being raised upon
Exponent: The term/variable is raised by a term. AKA Power
EXPONENT
BASE
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Rational Exponents

3. THE EXPONENT
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4. NTH ROOT RULE M is the power (exponent) N is the root A is the base
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Rational Exponents

5. RULES Another way of writing is 251/2.
is written in radical expression form.
251/2 is written in rational exponent form.
Why is square root of 25 equals out of 25 raised to ½ power?
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Rational Exponents

6. EXAMPLE 1 Evaluate 43/2 in radical form and simplify.
Rational Exponents

7. Evaluate 43/2 in radical form and simplify.
EXAMPLE 1
Evaluate 43/2 in radical form and simplify.
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8. EXAMPLE 2 Evaluate 41/2 in radical form and simplify.
Rational Exponents

9. YOUR TURN Evaluate (–27)2/3 in radical form and simplify.
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10. EXAMPLE 3 Evaluate –274/3 in radical form and simplify.
Use calculator to check
Hint: Remember, the negative is OUTSIDE of the base
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11. EXAMPLE 4 Evaluate in radical form and simplify. 1/15/2019 12:58 AM
Rational Exponents

12. DROP AND SWAP NTH ROOT RULE M is the power (exponent) N is the root
A is the base
DROP AND SWAP
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13. EXAMPLE 5 Evaluate (27)–2/3 in radical form and simplify.
Rational Exponents

14. EXAMPLE 6 Evaluate (–64)–2/3 in radical form and simplify.
Rational Exponents

15. YOUR TURN Evaluate in radical form and simplify. 1/15/2019 12:58 AM
Rational Exponents

16. PROPERTIES OF EXPONENTS
Product of a Power:
Power of a Power:
Power of a Product:
Negative Power Property:
Quotient Power Property:
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17. If the BASES are the same, ADD the powers
EXAMPLE 7
Simplify
Saying goes: BASE, BASE, ADD
If the BASES are the same, ADD the powers
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18. EXAMPLE 8
Simplify
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19. YOUR TURN
Simplify
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20. EXAMPLE 9 Simplify Saying goes: POWER, POWER, MULTIPLY
If the POWERS are near each other, MULTIPLY the powers – usually deals with PARENTHESES
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21. EXAMPLE 10
Simplify
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22. YOUR TURN
Simplify
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23. EXAMPLE 11
Simplify
Saying goes: When dividing an expression with a power, SUBTRACT the powers.
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24. EXAMPLE 12
Simplify
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25. EXAMPLE 13
Simplify
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Rational Exponents