Fractions, Negative Exponeats, Linear Expressions

(-9)^5

(-9)(-9)(-9)(-9)(-9)

more work #1

(2×5 × 10^8)(2×10^4) 2×5×2×10^8×10^4 = 5×10^12

properties of integer exponeats

(a^m)^n = a^n×a^m a^m/a^n= ^n-^m a^0 = 1

-2^4

-2×2×2×2

Simplifying fractions #2

15/35 = 3×5/7×5= 3/7

(-4×10^4)^2

16 × 10^8

simplifying fractions #3

180/140 = 20×9/20×7= 9/7

Multiplying Fractions #3

1×6/8×12 = 6/96 = 6/96 = 1/16

Dividing Fractions #3

1÷5/4÷6= 1×6/4×5 = 6/20

Multiplying Fractions #2

2×2/8×12 = 2/96= 1/48

2^3

2×2×2

linear expression #2

3(-3x+2)-2(x-1)+4x -9x+6 - 2x+2+4x -11x +4x = -7x +8

linear expression ex #1 (ax+b)

4-2x = -2x +4

pemdas #2

5-(1+7+1)÷11-2) 5-(9)/(9) 5-1=4

pemdas #1

54 + 6 ×(8/8)/6 54 + 6 × 1 ÷ 6 6÷6 = 1+54 = 55

Dividing Fractions #1

5÷7/14÷2 = 5×2/14×7 = 5/49

Multiplying Fractions #1

8×1/9×9= 8/81

An example of simplifying fractions #1

9/5 = 3×3/3×5

Dividing Fractions #2

9÷1/10÷3 = 9×3/10×1 = 27/10

GCF

Greatest multiple that goes into the numerator and dominator

order of operations

PEMDAS (parenthesis, Exponents, Multiplication, Division, Addition, Subtraction)

equivalent

Two expressions that are equal to each other.

negative exponents

With a negative exponent, take the reciprocal of the base and change the exponent to be positive x −a=1/x a Ex. 2 −3=1/2 3=1/8

improper fractions

a fraction with its numerator equal to or greater than its denominator/ anything equal to or greater than 1

Proper fractions

anything less than 1

equivelent fractions

a×c/b×c = a/b

reduced fraction

fraction that is fully simplified.

Simplification

reducing the expression, making them minimalist

quotient

the answer to a division problem

product

the answer to a multiplication problem

reciprocal of fraction

when the denominator and numerator are flipped

linear expression with variables #1

x-4y+8 (x=-1,y=5) -1 -4×5+8 -1-20+8= -2+8=-13