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SURF-MATHIC

SURF-MATHIC


Properties of Exponents:
Definition of exponent: An exponent tells you how
many times multiply a number by itself.

Addition property:
Addition: Thefirst rule to remember when adding with exponents is the order of operations; parenthesis, exponents, multiplication, division, addition and subtraction.

Examples:
1. 5^3 + 6^
2. 5*5*5=12 5
3. 6*6*=3
4. 125+ 36 = 161

Multiplication property:
Exponents show that the exponent tells us to multiply a number by itself that many times.
Examples:
1. (2*3) * 4 = 2* (3*4)2. (1+2) + 4 = 1+ (2+4)
3. 4+7=7+4
4. A*(b+c) = (a * b) + (a*c)

Division property:
In mathematics, exponents are algebraic expression usually written in the C^x where “C” is thebase and “x” is the exponent.

Examples:
1) (x^m)^n=x^(m*n)
2) X^(-1) = 1/(x^n)
3) X^2*x^5=x^(2+50=x^7
4) (x*y)^m=X^m*y6m

Properties of sings:
Property of addition:The sum of two positive integers is positive. The sum of two negative integers is negative.

Examples:
1) -12+(-31)=-43
2) 7+(-18)=-11
3) a+(b+c)=(a+b)+c
4) a + b=b + a

Property of multiplication:

To explain the rules for multiplication of signed numbers we recall that multiplication of whole numbers may be thought of as shortened addition.Examples:
1) 4(5)=5+5+5+5=20
2) -4(-5)=(-5)-(-5)-(-5)-(-5)
3) 4(-2)-(-5)-(6)-(-3)=-720
4) 3(-4)=(-4) + (-4)+(-4)+(-4)

Division property:
Because division is the inverse ofmultiplication, we can quickly develop the rules for division of signed numbers by comparison.

Examples:
1) 3(-4)-(-12) = -4
2) 3(-4)=-12=3
3) 15+-5
4) -2 (-3)/-6Practice problems:
1) 5(-8) =? A)24
2) -7(3) (2) =? B)-40
3) 6(-1) (-4) =? C) -720
4) -2(3) (-4) (5)(-6)=? D)-42