0-4 nth Roots and Real Exponents
Evaluate.
1. SOLUTION: 3. SOLUTION: 5. SOLUTION: Because there is no real number that can be raised to the fourth power to produce –81,
is not a real number.
7. SOLUTION: Simplify.
9. SOLUTION: Because the index is odd, it is not necessary to use absolute value.
11. SOLUTION: You are taking an even root of an even power, but the result is an even power, so you do not need to use the
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absolute value of y .
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0-4 Because
nth Roots
andisReal
the index
odd, it Exponents
is not necessary to use absolute value.
11. SOLUTION: You are taking an even root of an even power, but the result is an even power, so you do not need to use the
2
absolute value of y .
13. SOLUTION: While you are taking an even root of an even power, the result is an even power, so you do not need to use the
2
absolute value of y .
15. SOLUTION: Because you are taking an even root of an even power and the result is an odd power, you must use the absolute
3
value of a .
Simplify.
17. SOLUTION: Because you are taking an even root of an odd power, it is not necessary to use absolute value. Therefore,
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simplifies to or .
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Because you are taking an even root of an even power and the result is an odd power, you must use the absolute
0-4 nth Roots
and Real Exponents
3
value of a .
Simplify.
17. SOLUTION: Because you are taking an even root of an odd power, it is not necessary to use absolute value. Therefore,
simplifies to or .
19. SOLUTION: 21. SOLUTION: eSolutions Manual - Powered by Cognero
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0-4 nth Roots and Real Exponents
21. SOLUTION: Evaluate.
25. SOLUTION: 27. SOLUTION: 29. MUSIC The note progression of the twelve tone scale is comprised of a series of half tones. In order for an
instrument to be “in tune,” the frequency of each note has an optimum ratio with the frequency of middle C, called
the perfect 1st.
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0-4 nth Roots and Real Exponents
29. MUSIC The note progression of the twelve tone scale is comprised of a series of half tones. In order for an
instrument to be “in tune,” the frequency of each note has an optimum ratio with the frequency of middle C, called
the perfect 1st.
The optimum frequency ratio r, expressed as a decimal, can be calculated using
, where n is the number
of half tones the note is above the perfect 1st, including the note itself.
a. Approximate the optimum frequency ratio of the middle 3rd with the perfect 1st.
b. Without the use of a calculator, approximate the optimum frequency ratio of the perfect 8th and the perfect 1st.
Justify your answer.
SOLUTION: a. The middle 3rd is 4 half tones above the perfect 1st, so evaluate
for n = 4.
The optimum frequency ratio of the middle 3rd with the perfect 1st is 1.26.
b. The perfect 8th is 12 half tones above the perfect 1st. Evaluating
for n = 12, yields
1
, which simplifies to 2 or 2.
Simplify.
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The optimum frequency ratio of the middle 3rd with the perfect 1st is 1.26.
b. The perfect 8th is 12 half tones above the perfect 1st. Evaluating
for n = 12, yields
0-4 nth Roots and Real Exponents
1
, which simplifies to 2 or 2.
Simplify.
31. SOLUTION: Because the index is odd, it is not necessary to use absolute value.
33. SOLUTION: Because you are taking an even root of an even power and the result is an odd power, you must use the absolute
3
value of y and z . It is not necessary to use absolute value on x because
is an even root of an odd power.
35. SOLUTION: Because the index is odd, it is not necessary to use absolute value.
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