StarterStarter

Simplify the following:Simplify the following:

2a + 3b – 7a + b2a + 3b – 7a + b

4c4c22 – 3c + 6c – 3c + 6c22 – 8c – 8c

5de + 6fd – 2ef – 6ed5de + 6fd – 2ef – 6ed

-5a + 4b

10c2 – 11c

-de + 6df – 2ef

StarterStarter

Simplify the Simplify the following:following:

2a . 3b . – 8c2a . 3b . – 8c

5d . - 6e + 6e . 2d5d . - 6e + 6e . 2d

18y15xy

-48abc

-18de

65x

53 2x4x 8x8

2ab3abb 52 82b6a

Note 5: ExponentsNote 5: Exponents

When multiplying numbers with the same base

Examples:

add the powers

46 2a12a 26a

c7abcb14a

3

5222ab

When dividing numbers with the same base

Examples:

subtract the powers

The power of a product is the

Examples:

product of the powers

3(b.c) 33.cb

The power of a quotient is the

Examples:

quotient of the powers

3

x2

3x8

When taking an exponent of another exponent

Examples:

multiply the powers

25)(b 10b 325 )b(6a 615b216a

Any base to the power of zero

Examples:

equals one

042 )c(3a 1

To find the square root of an algebraic To find the square root of an algebraic expression:expression:

half the powerhalf the power square root the numbersquare root the number

Examples:Examples: SimplifySimplify

1636x 14

6

25t16s

= 6x87

3

5t4s

Combined operations

32 53 4

57 4

32

3 4

xyx y

xy x y

6 8 3 15

2 2 7 20

4 27

9 4

x y x y

x y x y

3

=9 23

9 22

3x y

x y

= 3y

=

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