Exponent Rules Worksheet: Math Practice Problems

Формула:
𝑎𝑛 ∙ 𝑎𝑚
= 𝑎𝑛+𝑚
Примеры:
1) 4 ∙ 4 = 4
= 48
−3
5
−3+5
2) 4 ∙ 4 = 4
= 42 = 16
𝑎𝑛 : 𝑎𝑚 = 𝑎𝑛−𝑚
1)510 : 58 = 510−8 = 52 = 25
2) 52 : 5−2 = 52−(−2) = 54 = 625
(𝑎𝑛 )𝑚 = 𝑎𝑛∙𝑚
1)(23 )4 = 23∙4 = 212
2) (2−3 )2 = 2−3∙2 = 2−6
3) (2−3 )−5 = 2−3∙(−5) = 215
2 2 22 4
( ) = 2=
3
3
9
(2 ∙ 3 ∙ 4)2 = 22 ∙ 32 ∙ 42 = 4 ∙ 9 ∙ 16 = 576
3
𝑎 𝑛 𝑎𝑛
( ) = 𝑛
𝑏
𝑏
(𝑎 ∙ 𝑏 ∙ 𝑐)𝑛
= 𝑎𝑛 ∙ 𝑏 𝑛 ∙ 𝑐 𝑛
1
𝑎−𝑛 = 𝑛
𝑎
𝑛
5
3+5
1
1
3
1
27
1) 3−3 = 3 =
1
(−2)3
=−
1
( )
4
2
4
42
= ( ) = 2 = 16
1
1
Примеры:
1) 43 ∙ 45 = 43+5 = 48
2) 4−3 ∙ 45 = 4−3+5 = 42 = 16
𝑎𝑛 : 𝑎𝑚 = 𝑎𝑛−𝑚
1)510 : 58 = 510−8 = 52 = 25
2) 52 : 5−2 = 52−(−2) = 54 = 625
(𝑎𝑛 )𝑚 = 𝑎𝑛∙𝑚
1)(23 )4 = 23∙4 = 212
2) (2−3 )2 = 2−3∙2 = 2−6
3) (2−3 )−5 = 2−3∙(−5) = 215
2 2 22 4
( ) = 2=
3
3
9
(2 ∙ 3 ∙ 4)2 = 22 ∙ 32 ∙ 42 = 4 ∙ 9 ∙ 16 = 576
𝑛
𝑎 −𝑛
𝑏
( ) =( )
𝑏
𝑎
𝑏𝑛
= 𝑛
𝑎
1 −4
1
1
3
1
27
1) 3−3 = 3 =
1
(−2)3
=−
Формула:
𝑎𝑛 ∙ 𝑎𝑚
= 𝑎𝑛+𝑚
Примеры:
1) 4 ∙ 4 = 4
= 48
−3
5
−3+5
2) 4 ∙ 4 = 4
= 42 = 16
𝑎𝑛 : 𝑎𝑚 = 𝑎𝑛−𝑚
1)510 : 58 = 510−8 = 52 = 25
2) 52 : 5−2 = 52−(−2) = 54 = 625
(𝑎𝑛 )𝑚 = 𝑎𝑛∙𝑚
1)(23 )4 = 23∙4 = 212
2) (2−3 )2 = 2−3∙2 = 2−6
3) (2−3 )−5 = 2−3∙(−5) = 215
2 2 22 4
( ) = 2=
3
3
9
(2 ∙ 3 ∙ 4)2 = 22 ∙ 32 ∙ 42 = 4 ∙ 9 ∙ 16 = 576
=
2) ( )
=
3
3 −3
2)(−2)−3 =
;
Вычислите:
1) 56 ∙ 521 =
2) 3−20 ∙ 315 =
3) 8−2 ∙ 8−1 =
1)225 : 221 =
2) 6−2 : 66 =
3) 7−2 : 7−1 =
1)(4−2 )−2 =
2) (5−6 )2 =
3) (3−5 )−5 =
1 3
( ) =
7
1)(2𝑎𝑏)5 =
2)(−3𝑎 −2 𝑏)3
1)5−3 =
2) (−4)−3 =
8
−2
1
( )
4
2
2
4
4
= ( ) = 2 = 16
1
1
1 −4
𝑎 𝑛 𝑎𝑛
( ) = 𝑛
𝑏
𝑏
(𝑎 ∙ 𝑏 ∙ 𝑐)𝑛
= 𝑎𝑛 ∙ 𝑏 𝑛 ∙ 𝑐 𝑛
1
𝑎−𝑛 = 𝑛
𝑎
=
2) ( )
=
8
5
3+5
1
1
3
1
27
1) 3−3 = 3 =
1
(−2)3
=−
;
2)(−2)−3 =
Примеры:
1) 43 ∙ 45 = 43+5 = 48
2) 4−3 ∙ 45 = 4−3+5 = 42 = 16
𝑎𝑛 : 𝑎𝑚 = 𝑎𝑛−𝑚
1)510 : 58 = 510−8 = 52 = 25
2) 52 : 5−2 = 52−(−2) = 54 = 625
(𝑎𝑛 )𝑚 = 𝑎𝑛∙𝑚
1)(23 )4 = 23∙4 = 212
2) (2−3 )2 = 2−3∙2 = 2−6
3) (2−3 )−5 = 2−3∙(−5) = 215
2 2 22 4
( ) = 2=
3
3
9
(2 ∙ 3 ∙ 4)2 = 22 ∙ 32 ∙ 42 = 4 ∙ 9 ∙ 16 = 576
𝑎 −𝑛
𝑏
( ) =( )
𝑏
𝑎
𝑏𝑛
= 𝑛
𝑎
21
1 −4
1)( )
=
2) ( )
=
3
3 −3
8
Формула:
𝑎𝑛 ∙ 𝑎𝑚
= 𝑎𝑛+𝑚
𝑎 𝑛 𝑎𝑛
( ) = 𝑛
𝑏
𝑏
(𝑎 ∙ 𝑏 ∙ 𝑐)𝑛
= 𝑎𝑛 ∙ 𝑏 𝑛 ∙ 𝑐 𝑛
1
𝑎−𝑛 = 𝑛
𝑎
Вычислите:
1) 5 ∙ 5 =
2) 3−20 ∙ 315 =
3) 8−2 ∙ 8−1 =
1)225 : 221 =
2) 6−2 : 66 =
3) 7−2 : 7−1 =
1)(4−2 )−2 =
2) (5−6 )2 =
3) (3−5 )−5 =
1 3
( ) =
7
1)(2𝑎𝑏)5 =
2)(−3𝑎 −2 𝑏)3
1)5−3 =
2) (−4)−3 =
6
8
1 −2
4 2 42
( ) = ( ) = 2 = 16
4
1
1
𝑎 −𝑛
𝑏
( ) =( )
𝑏
𝑎
𝑏𝑛
= 𝑛
𝑎
𝑛
1)( )
3
3 −3
3
𝑛
1)( )
8
Формула:
𝑎𝑛 ∙ 𝑎𝑚
= 𝑎𝑛+𝑚
𝑎 𝑛 𝑎𝑛
( ) = 𝑛
𝑏
𝑏
(𝑎 ∙ 𝑏 ∙ 𝑐)𝑛
= 𝑎𝑛 ∙ 𝑏 𝑛 ∙ 𝑐 𝑛
1
𝑎−𝑛 = 𝑛
𝑎
21
8
−2
𝑎 −𝑛
𝑏
( ) =( )
𝑏
𝑎
𝑏𝑛
= 𝑛
𝑎
2)(−2)−3 =
;
Вычислите:
1) 5 ∙ 5 =
2) 3−20 ∙ 315 =
3) 8−2 ∙ 8−1 =
1)225 : 221 =
2) 6−2 : 66 =
3) 7−2 : 7−1 =
1)(4−2 )−2 =
2) (5−6 )2 =
3) (3−5 )−5 =
1 3
( ) =
7
1)(2𝑎𝑏)5 =
2)(−3𝑎 −2 𝑏)3
1)5−3 =
2) (−4)−3 =
6
1
1
3
1
27
1) 3−3 = 3 =
1
(−2)3
=−
;
2)(−2)−3 =
Вычислите:
1) 56 ∙ 521 =
2) 3−20 ∙ 315 =
3) 8−2 ∙ 8−1 =
1)225 : 221 =
2) 6−2 : 66 =
3) 7−2 : 7−1 =
1)(4−2 )−2 =
2) (5−6 )2 =
3) (3−5 )−5 =
1 3
( ) =
7
1)(2𝑎𝑏)5 =
2)(−3𝑎 −2 𝑏)3
1)5−3 =
2) (−4)−3 =
8
1 −2
4 2 42
( ) = ( ) = 2 = 16
4
1
1
1 −4
1)( )
=
2) ( )
=
3
3 −3
8