1. Nth roots and Rational Exponents
Section 5.1
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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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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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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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6. EXAMPLE 1 Evaluate 43/2 in radical form and simplify.

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

8. EXAMPLE 2 Evaluate 41/2 in radical form and simplify.

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.
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12. NTH ROOT RULE M is the power (exponent) N is the root A is the base
M is the power (exponent)
N is the root
A is the base
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Rational Exponents

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. 6/26/2018 5:52 AM
Rational Exponents