6.1: Integer Exponents and Scientific Notation
Product Rule for Exponents:
If m and n are natural numbers and a is any real number, then
am*an=am+n
In words. when multiplying powers of like bases, keep the same base and add the exponents.
Zero Exponent:
If a is any nonzero real number, then
a0=1
Negative Exponent:
For any natural number n and any nonzero real number a,
a-n=1/an
Quotient Rule for Exponents:
If a is any nonzero real number and m and n are integers, then
am/an= am-n
Power Rules for Exponents:
If a and b are real umbers and m and n are integers, then
(a) (am)^n= amn
(b) (ab)^m=ambm
( c) (a/b)^m=am/bm when b is not equal to zero
Scientific Notation:
A number is written in scientific notation when it is express in the form
a*10n
Converting to Scientific Notation:
Step 1. Position the decimal point. Place a caret ^, to the right of the first nonzero digit, where the decimal point will be placed.
Step 2. Determine the numeral for the exponent. Count the number of Digits from the decimal point to the caret. This number gives the absolute value of the exponent on 10.
Step 3. Determine the sign for the exponent. Decide whether multiplying by 10n should make the result of Step 1 larger or smaller. The exponent should be positive to make the result larger, it should be negative to make the result smaller.
Converting From Scientific Notation:
Multiplying a number by a positive power of 10 makes the number larger, so move the decimal point to the right n places if n is positive in 10n.
Multiplying by a negative power of 10 makes a number smaller, so more the deimal point to the left n places if n is negative.
If n is 0, leave the decimal point where it is.
Product Rule for Exponents:
If m and n are natural numbers and a is any real number, then
am*an=am+n
In words. when multiplying powers of like bases, keep the same base and add the exponents.
Zero Exponent:
If a is any nonzero real number, then
a0=1
Negative Exponent:
For any natural number n and any nonzero real number a,
a-n=1/an
Quotient Rule for Exponents:
If a is any nonzero real number and m and n are integers, then
am/an= am-n
Power Rules for Exponents:
If a and b are real umbers and m and n are integers, then
(a) (am)^n= amn
(b) (ab)^m=ambm
( c) (a/b)^m=am/bm when b is not equal to zero
Scientific Notation:
A number is written in scientific notation when it is express in the form
a*10n
Converting to Scientific Notation:
Step 1. Position the decimal point. Place a caret ^, to the right of the first nonzero digit, where the decimal point will be placed.
Step 2. Determine the numeral for the exponent. Count the number of Digits from the decimal point to the caret. This number gives the absolute value of the exponent on 10.
Step 3. Determine the sign for the exponent. Decide whether multiplying by 10n should make the result of Step 1 larger or smaller. The exponent should be positive to make the result larger, it should be negative to make the result smaller.
Converting From Scientific Notation:
Multiplying a number by a positive power of 10 makes the number larger, so move the decimal point to the right n places if n is positive in 10n.
Multiplying by a negative power of 10 makes a number smaller, so more the deimal point to the left n places if n is negative.
If n is 0, leave the decimal point where it is.
This is for the tutorial, but I someone forgot to share it with me so I thought it would be helpful to have on the blog!
ReplyDeleteDividing fractions with variables & exponents is tricky. This website explains very well.
ReplyDeletehttp://www.tutorvista.com/math/dividing-fractions-with-variables-and-exponents
Remember, a^-0 = -1
ReplyDelete