6.7E: Exercises
- Page ID
- 30546
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More Practice with Exponents in Quotients
Quotients
Exercise \(\PageIndex{89}\)
\( \bigstar \) Simplify. (Assume all variables represent nonzero numbers.)
1. \( \displaystyle \frac { 10 ^ { 2 } \cdot 10 ^ { 4 } } { 10 ^ { 5 } } \\[6pt]\) 2. \( \displaystyle \frac { 7 ^ { 5 } \cdot 7 ^ { 9 } } { 7 ^ { 2 } } \\[6pt]\) 3. \( \displaystyle \frac { a ^ { 8 } \cdot a ^ { 6 } } { a ^ { 5 } } \\[6pt]\) 4. \( \displaystyle \frac { b ^ { 4 } \cdot b ^ { 10 } } { b ^ { 8 } } \\[6pt]\) |
5. \( \displaystyle\frac { a ^ { 8 } \cdot a ^ { - 3 } } { a ^ { - 6 } } \\[6pt]\) 6. \( \displaystyle\frac { b ^ { - 10 } \cdot b ^ { 4 } } { b ^ { - 2 } } \\[6pt]\) 7. \( \displaystyle\frac { 25 x ^ { - 3 } y ^ { 2 } } { 5 x ^ { - 1 } y ^ { - 3 } } \\[6pt]\) 8. \( \displaystyle\frac { - 9 x ^ { - 1 } y ^ { 3 } z ^ { - 5 } } { 3 x ^ { - 2 } y ^ { 2 } z ^ { - 1 } } \\[6pt]\) |
9. \( \displaystyle \frac { 40 x ^ { 5 } y ^ { 3 } z } { 4 x ^ { 2 } y ^ { 2 } z } \\[6pt]\) 10. \( \displaystyle \frac { 8 x ^ { 2 } y ^ { 5 } z ^ { 3 } } { 16 x ^ { 2 } y z } \\[6pt]\) 11. \( \displaystyle \frac { 24 a ^ { 8 } b ^ { 3 } ( a - 5 b ) ^ { 10 } } { 8 a ^ { 5 } b ^ { 3 } ( a - 5 b ) ^ { 2 } } \\[6pt]\) 12. \( \displaystyle \frac { 175 m ^ { 9 } n ^ { 5 } ( m + n ) ^ { 7 } } { 25 m ^ { 8 } n ( m + n ) ^ { 3 } } \\[6pt]\) |
- Answers to odd exercises.
-
1. \(10 \\[6pt]\)
3. \(a^{9} \)
5. \(a^{11} \\[6pt]\)
7. \( \displaystyle\frac { 5 y ^ { 5 } } { x ^ { 2 } } \)
9. \(10x^{3}y \\[6pt]\)
11. \(3a^{3}(a − 5b)^{8} \)
Powers of Quotients
Exercise \(\PageIndex{90} \)
\( \bigstar \) Simplify. (Assume all variables represent nonzero numbers.)
1. \(\left( \displaystyle \frac { - 3 a b ^ { 2 } } { 2 c ^ { 3 } } \right) ^ {3 } \\[6pt]\) 2. \(\left( \displaystyle \frac { - 10 a ^ { 3 } b } { 3 c ^ { 2 } } \right) ^ {2 } \\[6pt]\) 3. \(\left( \displaystyle \frac { - 2 x y ^ { 4 } } { z ^ { 3 } } \right) ^ {4 } \\[6pt]\) 4. \(\left( \displaystyle \frac { - 7 x ^ { 9 } y } { z ^ { 4 } } \right) ^ {3 } \) |
5. \(\left( \displaystyle \frac { 12 x ^ { 3 } y ^ { 2 } z } { 2 x ^ { 7 } y z ^ { 8 } } \right) ^ {3 } \\[6pt]\) 6. \(\left( \displaystyle \frac { 150 x y ^ { 8 } z ^ { 2 } } { 90 x ^ { 7 } y ^ { 2 } z } \right) ^ {2 } \\[6pt]\) 7. \(\left( \displaystyle \frac { 2 x ^ { - 3 } z } { y ^ { 2 } } \right) ^ {- 5 } \\[6pt]\) 8. \(\left( \displaystyle \frac { 5 x ^ { 5 } z ^ { - 2 } } { 2 y ^ { - 3 } } \right) ^ {- 3 } \) |
9. \(\left( \displaystyle \frac { x y ^ { 2 } } { z ^ { 3 } } \right) ^ {3 } \\[6pt]\) 10. \(\left( \displaystyle \frac { 2 x ^ { 2 } y ^ { 3 } } { z } \right) ^ {4 } \\[6pt]\) 11. \(\left( \displaystyle \frac { - 9 a ^ { - 3 } b ^ { 4 } c ^ { - 2 } } { 3 a ^ { 3 } b ^ { 5 } c ^ { - 7 } } \right) ^ {- 4 } \\[6pt]\) 12. \(\left( \displaystyle \frac { - 15 a ^ { 7 } b ^ { 5 } c ^ { - 8 } } { 3 a ^ { - 6 } b ^ { 2 } c ^ { 3 } } \right) ^ {- 3 } \) |
- Answers to odd exercises:
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1. \(- \displaystyle\frac { 27 a ^ { 3 } b ^ { 6 } } { 8 c ^ { 9 } } \\[6pt]\)
3. \( \displaystyle\frac { 16 x ^ { 4 } y ^ { 16 } } { z ^ { 12 } } \)
5. \( \displaystyle\frac { 216 y ^ { 3 } } { x ^ { 12 } z ^ { 21 } } \\[6pt]\)
7. \( \displaystyle\frac { x ^ { 15 } y ^ { 10 } } { 32 z ^ { 5 } } \)
9. \( \displaystyle\frac { x ^ { 3 } y ^ { 6} } { z ^ { 9 } } \\[6pt]\)
11. \( \displaystyle\frac { a ^ { 24 } b ^ { 4 } } { 81 c ^ { 20 } } \)