Name: __________________________
Score:
Answer key
Algebra: M
Base and Exponent
ܽ ଼
1) ቀ ቁ
ܾ
ࢇ
‫= ݁ݏܽܤ‬
࢈
భ
2) (‫ ݔ‬+ ‫)ݕ‬ర
3) 4 ௭ାଷ
‫ ࢞ = ݁ݏܽܤ‬+ ࢟
‫ = ݐ݊݁݊݋݌ݔܧ‬ૡ
‫ = ݁ݏܽܤ‬૝
‫= ݐ݊݁݊݋݌ݔܧ‬
‫ ࢠ = ݐ݊݁݊݋݌ݔܧ‬+ ૜
2 ௔
4) ൬ ൰
3
5) (2‫ ݌‬+ ‫)ݍ‬య
6) 5್
‫ = ݁ݏܽܤ‬૛࢖ + ࢗ
‫ = ݁ݏܽܤ‬૞
‫= ݐ݊݁݊݋݌ݔܧ‬
‫= ݐ݊݁݊݋݌ݔܧ‬
‫= ݁ݏܽܤ‬
૛
૜
‫ࢇ = ݐ݊݁݊݋݌ݔܧ‬
మ
݉ య
7) ቀ ቁ
݊
࢓
‫= ݁ݏܽܤ‬
࢔
૛
‫= ݐ݊݁݊݋݌ݔܧ‬
૜
ସ
10) (ܽ − 2)
‫ ࢇ = ݁ݏܽܤ‬− ૛
૚
૝
భ
ೌ
૚
૜
8) (‫ ݔ‬+ 2)ହ
‫ ࢞ = ݁ݏܽܤ‬+ ૛
‫ = ݐ݊݁݊݋݌ݔܧ‬૞
య
11) 7మ
‫ = ݁ݏܽܤ‬ૠ
૜
૛
‫ = ݐ݊݁݊݋݌ݔܧ‬૝
‫= ݐ݊݁݊݋݌ݔܧ‬
13) 5௠ିଶ
‫ି ݑ‬ଷ
14) ቀ ቁ
‫ݒ‬
࢛
‫= ݁ݏܽܤ‬
࢜
‫ = ݐ݊݁݊݋݌ݔܧ‬−૜
‫ = ݁ݏܽܤ‬૞
‫ ࢓ = ݐ݊݁݊݋݌ݔܧ‬− ૛
16) (݉ + 5݊)ି௤
17) (1 + 2‫)݌‬
‫ ࢓ = ݁ݏܽܤ‬+ ૞࢔
‫ = ݁ݏܽܤ‬૚ + ૛࢖
−ࢇ
‫= ݐ݊݁݊݋݌ݔܧ‬
࢈
‫ = ݐ݊݁݊݋݌ݔܧ‬−ࢗ
షೌ
್
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−3 ିଶ
9) ൬ ൰
4
−૜
‫= ݁ݏܽܤ‬
૝
ࢇ
࢈
‫ = ݐ݊݁݊݋݌ݔܧ‬−૛
2 ௔
12) ൬ ൰
3
૛
‫= ݁ݏܽܤ‬
૜
‫ࢇ = ݐ݊݁݊݋݌ݔܧ‬
15) (‫ ݌‬+ ‫)ݍ‬଴
‫ ࢖ = ݁ݏܽܤ‬+ ࢗ
‫ = ݐ݊݁݊݋݌ݔܧ‬૙
7 ିହ
18) ൬ ൰
9
ૠ
ૢ
‫ = ݐ݊݁݊݋݌ݔܧ‬−૞
‫= ݁ݏܽܤ‬
Name: __________________________
Answer key
Score:
Algebra: E1
Product Rule
‫ ݖ‬ଶ · ‫଺ି ݖ‬
1)
=
4)
2)
૚
ࢠ૝
݊ିଽ · ݊ଵ଴
݈ି଼ · ݈ିଶ
5)
‫ݍ · ଼ݍ‬ଽ
10)
8)
‫ ݕ‬ସ · ‫଻ି ݕ‬
16)
‫ି ݓ · ଻ ݓ‬ଶ
‫ି ݒ‬ହ · ‫ି ݒ‬ସ
=
૚
࢜ૢ
ܿ ି଼ · ܿ ଺
14)
=
9)
=
20)
= ࢇ૟
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‫ି ݔ‬ଵ଴ · ‫଻ ݔ‬
૚
࢞૜
݀଻ · ݀ହ
12)
= ࢊ૚૛
݉ ି଻ · ݉ିଽ
15)
=
=
21)
૚
࢓૚૟
‫ ݐ · ଼ି ݐ‬ସ
18)
૚
࢘૚૟
ܽ ଽ · ܽ ିଷ
‫ݏ‬ଷ · ‫଺ݏ‬
=
૚
ࢉ૛
‫ି ݎ · ଺ି ݎ‬ଵ଴
17)
૚
࢘ૠ
= ࢙ૢ
= ࢎ૛
= ࢝૞
19)
ℎ ଺ · ℎିସ
11)
૚
࢟૜
=
6)
૚
࢑૚૛
݃ିଷ · ݃ଵ଴
‫ି ݎ‬ସ · ‫ି ݎ‬ଷ
=
= ࢍૠ
= ࢗ૚ૠ
13)
݇ ି଻ · ݇ ିହ
=
૚
࢒૚૙
=
3)
= ࢛૚૛
= ࢔૚
7)
‫ݑ‬ଵ଴ · ‫ ݑ‬ଶ
૚
࢚૝
ℎ ହ · ℎଽ
= ࢎ૚૝
Name: __________________________
Answer key
Score:
Algebra: M1
Product Rule
1)
4݀ ି଺ · 3݀ ି଺
=
4)
2)
૚૛
ࢊ૚૛
6‫ି݌‬ହ · 8‫ · ଺݌‬4‫଼݌‬
2݃ିହ · ݃ଽ
= ૛ࢍ૝
10) 3݈ · 5݈ ସ · 2݈ ଺
= ૜૙࢒૚૚
13) 3‫ ݐ‬ସ · 6‫ · ݐ‬8‫଺ ݐ‬
= ૚૝૝࢚૚૚
16) 4‫ି ݖ‬ଷ · 6‫ ݖ‬ଽ · ‫ݖ‬
= ૛૝ࢠૠ
3)
5)
7ℎସ · 3ℎିଶ · 9ℎ
6)
= ૚ૡૢࢎ૜
8)
3௪ · 3ସ · 3ି଻
= ૜࢝ି૜
11) 3‫ ݍ‬ହ ‫ ݎ‬ସ (5‫ ݍ‬ସ ‫ ݎ‬ଷ )(3‫ ݍ‬ଶ ‫ ݎ‬ଶ )
= ૝૞ࢗ૚૚ ࢘ૢ
14) 2ିସ · 2௪ · 2଺
= ૛࢝ା૛
17) ‫ ݎ‬ହ ‫ି ݎ · ଺ ݏ‬ସ ‫ି ݏ‬ଶ · ‫ ݏ ଺ ݎ‬ସ
= ࢘ ૠ ࢙ૡ
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8௭ · 8ିହ · 8଼
= ૡࢠା૜
= ૚૛࢈૛ ࢉ૟
= ૚ૢ૛࢖ૢ
7)
2ܾ ସ ܿ ହ (6ܾ ିଶ ܿ)
9ܿ · 7ܿ ଼
= ૟૜ࢉૢ
9)
݉ ସ ݊ିଶ (3଼݉݊ )
= ૜࢓૞ ࢔૟
12) 6‫ · ݏ‬4‫ି ݏ‬ହ
=
૛૝
࢙૝
15) 4‫ ݑ‬ସ ‫ ݒ‬ହ · ‫ି ݑ‬ଶ ‫ି ݒ‬ଷ · 3‫଺ ݒ ଼ ݑ‬
= ૚૛࢛૚૙ ࢜ૡ
18) 8݉ିହ · 5଼݉
= ૝૙࢓૜
Name: __________________________
Answer key
Score:
Algebra: E1
Quotient Rule
1)
4)
‫ݕ‬ଽ
‫ݕ‬ଷ
2)
= ࢘૛
= ࢚૚
‫଺ݔ‬
‫ݔ‬ସ
‫ݍ‬ଵ଴
‫ݍ‬ଷ
ℎ଼
ℎହ
5)
଼ܾ
ܾ଺
‫ݓ‬ଽ
10) ଺
‫ݓ‬
8)
= ࢜૞
݀ଽ
݀ସ
݃ସ
11) ଶ
݃
9)
ܿଽ
14) ଻
ܿ
݉ହ
12) ଶ
݉
= ࢓૜
‫݌‬ଷ
15) ଶ
‫݌‬
= ࢉ૛
17)
‫଺ݏ‬
‫ݏ‬ଶ
= ࢙૝
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‫ ݐ‬ଵ଴
‫଼ݐ‬
= ࢚૛
= ࢍ૛
= ࢛૞
‫଼ݒ‬
‫ݒ‬ଷ
= ࢎ૜
= ࢊ૞
= ࢝૜
‫଻ݑ‬
13) ଶ
‫ݑ‬
6)
= ࢗૠ
= ࢈૛
16)
3)
‫ݐ‬ହ
‫ݐ‬ସ
= ࢟૟
= ࢞૛
7)
‫଻ݎ‬
‫ݎ‬ହ
= ࢖૚
18)
݊ଵ଴
݊ହ
= ࢔૞
Name: __________________________
Answer key
Score:
Algebra: M1
Quotient Rule
1)
4)
4‫ି ݏ‬ଷ ‫ି ݐ‬ସ
8‫଼ ݐ ଺ ݏ‬
3‫ ݒ ଼ ݑ‬ସ
7‫ ݑ‬ହ ‫ ݒ‬ଶ
9‫݌‬ହ ‫ି ݍ‬ଶ
3)
5‫ି݌‬ଷ ‫଺ݍ‬
૚
= ૢ ૚૛
૛࢙ ࢚
૜࢛૜ ࢜૛
=
ૠ
=
7ܽ ିଷ ܾ ଽ
2ܽ ଶ ܾ ିହ
4݈ଽ ݉ସ
9݈ଷ ݉ଶ
=
7)
=
13)
=
8)
ૢ
8ܿ݀ ଽ
2ܿ ି଼ ݀ ସ
= ૝ࢉૢ ࢊ૞
8ܾ ି଺ ܿ ିହ
9ܾ ି଼ ܿ ିଶ
=
=
17)
9)
૝࢔ૡ
= ૞
࢓
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‫ି ݎ‬ସ ‫ ݏ‬ହ
‫ି ݏ ଼ି ݎ‬ଽ
5݉ି଻ ݊ହ
3݉ ିସ ݊ିହ
૞࢔૚૙
=
૜࢓૜
7‫ ݍ‬ହ ‫ି ݎ‬ସ
5‫଻ ݎ ଺ ݍ‬
12)
=
ૠ
૞ࢗ࢘૚૚
‫ ݕ‬ସ ‫ ݖ‬ଵ଴
‫ ݖݕ‬ହ
15)
ૡ࢝ૢ ࢞૚૛
૜
4݉݊ଽ
݉଺ ݊
ૢ࢖ૡ
૞ࢗૡ
= ࢘૝ ࢙૚૝
ૡ࢈૛
ૢࢉ૜
8‫ ݓ‬ସ ‫ ݔ‬ଶ
3‫ି ݓ‬ହ ‫ି ݔ‬ଵ଴
14)
= ૡ૛࢝ା૝
16)
૝࢒૟ ࢓૛
ૢ
3݃ିଽ ℎସ
8݃ି଺ ℎ଼
11)
૚
૝࢑૝ ࢒૞
8௪ 8଺
8ି௪ 8ଶ
6)
૜
=
ૡࢍ૜ ࢎ૝
ૠ࢜૚૜ ࢝૟
2݇ ହ ݈ିଵ଴
8݇ ଽ ݈ ିହ
10)
5)
ૠ࢈૚૝
૛ࢇ૞
9‫ି ݒ‬ଵ଴ ‫ ݓ‬ସ
7‫ ݒ‬ଷ ‫ ݓ‬ଵ଴
=
2)
= ࢟૜ ࢠ૞
‫ ݍ ଺ି݌‬ଶ
8‫݌‬ଵ଴ ‫ି ݍ‬ହ
18)
=
ࢗૠ
ૡ࢖૚૟
Name: __________________________
Answer key
Score:
Algebra: E1
Power Rule
1)
ሺ‫଼ି) ଻ି ݕ‬
2)
= ࢟૞૟
4)
ሺܿ ସ )ଷ
ሺܾ ଽ )ିହ
=
5)
= ࢉ૚૛
3)
૚
࢈૝૞
ሺ‫ି) ଼ି ݑ‬ଽ
ሺ‫ି ݒ‬ଷ )଼
=
6)
ሺ‫ ݖ‬ଽ )ି଻
= ࢛ૠ૛
=
7)
ሺ݇ ଼ )ଶ
= ࢑૚૟
10) ሺ‫ି݌‬ହ )ଽ
8)
ሺ‫ି ݐ‬ସ )ଵ଴
=
૚
࢚૝૙
11) ሺ‫ ݔ‬ଷ )ିଵ଴
9)
૚
࢜૛૝
૚
ࢠ૟૜
ሺ‫ି ݓ‬ଽ )ିଽ
= ࢝ૡ૚
12) ሺ‫ݏ‬ଵ଴ )ଶ
૚
࢞૜૙
= ࢙૛૙
13) ሺ݉଻ )ି଺
14) ሺܽଵ଴ )ସ
15) ሺℎ଻ )ଵ଴
૚
࢓૝૛
= ࢇ૝૙
= ࢎૠ૙
=
=
૚
࢖૝૞
16) ሺ݃ଽ )ି଼
=
૚
ࢍૠ૛
=
17) ሺ݀ ିଵ଴ )ି଻
= ࢊૠ૙
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18) ሺ‫ି ݍ‬ଽ )ହ
=
૚
ࢗ૝૞
Name: __________________________
Answer key
Score:
Algebra: M1
Power Rule
1)
ሺ‫ି ݏ‬ଽ ‫ି ݐ‬ଵ଴ )ସ
=
4)
2)
૚
૜૟
࢙ ࢚૝૙
ሺ4‫ି ݍ‬ଶ ‫ି) ଺ି ݎ‬ସ
=
5)
ࢗૡ ࢘૛૝
=
૛૞૟
7)
ሺ2‫ି ݓ ଺ ݒ‬ସ )ିଶ
࢝ૡ
= ૚૛
૝࢜
10) ሺ‫ ݏ ଼ି ݎ‬ହ )ିଷ
࢘૛૝
= ૚૞
࢙
13) ሺ݃ିଷ ℎଽ )ିଽ
=
ࢍ૛ૠ
ࢎૡ૚
16) ሺ6‫ି)ݖ ଼ ݕ‬ଷ
=
૚
૛૚૟࢟૛૝ ࢠ૜
ሺ6‫ ݓ‬ସ ‫ ݔ‬ହ )ିଷ
3)
૚
૛૚૟࢝૚૛ ࢞૚૞
ሺ3‫ି ݒ‬ଶ ‫ି ݓ‬ଷ )ିସ
࢛૚૞
=
૚૛૞࢜૚૛
6)
࢜ૡ ࢝૚૛
=
ૡ૚
8)
ሺ‫ି ݌‬ସ ‫ି) ଻ି ݍ‬ଵ଴
= ࢖૝૙ ࢗૠ૙
11) ሺ6‫ି ݔ‬ଽ ‫) ଺ ݕ‬ଷ
૛૚૟࢟૚ૡ
=
࢞૛ૠ
14) ሺ2‫ ݓ‬ଵ଴ ‫଻)ݔ‬
= ૚૛ૡ࢝ૠ૙ ࢞ૠ
17) ሺ5݇ ଺ ݈଺ )ଷ
= ૚૛૞࢑૚ૡ ࢒૚ૡ
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ሺ5‫ି ݑ‬ହ ‫ ݒ‬ସ )ିଷ
ሺ݃ହ ℎି଻ )଼
ࢍ૝૙
= ૞૟
ࢎ
9)
ሺ‫ ݎ ଻ି ݍ‬ଶ )ଷ
࢘૟
= ૛૚
ࢗ
12) ሺ‫ି ݕ‬ହ ‫ି ݖ‬ସ )ି଺
= ࢟૜૙ ࢠ૛૝
15) ሺܾ ଼ ܿ )଺
= ࢈૝ૡ ࢉ૟
18) ሺ2‫ି ݔ ଺ ݓ‬ଽ )ସ
=
૚૟࢝૛૝
࢞૜૟