P.2 Reading Guide-Math 1111
Exponents and Scientific Notation (pages 20-35)
---------------------------------------------------------------------------------------------------------1. Define the rules for exponents, with an example of each


The Product Rule when multiplying two powers that have the same base, you can add the exponents. Ex:
2^3*2^4= 2^6
 The Quotient Rule this says that to divide two exponents with the same base, you keep the base and subtract the powers. Ex:a^m/a^n= a^m-n


The Zero Exponent Rule basically says that any base with an exponent of zero is equal to one. Ex: b^0 = 1

 The Negative Exponent Rule
. A negative exponent means how many times to divide by the number. Example: 8-1 = 1 ÷ 8 = 1/8
= 0.125.


The Power Rule (Powers to powers) this says that to raise a power to a power you need to multiply the exponents. Ex: (a^m)^n = a^(mn)  The Product to Powers Rule tells us that when you multiply powers with the same base you just have to add the exponents.
Ex:a^m ? a^n = a^(m + n)



The Quotient to Powers Rule when you divide two powers with the same base, you subtract the exponents. a^m/a^n= a^(m-n)

2. List the four conditions for an exponential expression to be considered “simplified:”
a) There are no zero or negative exponents. b) No quotients are raised to powers. c) The same base appears only once in a product or quotient.
d) Numerical coefficients in a quotient do not have any common factor other than 1.

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3. State the definition of Scientific Notation.
Where a number is written in two parts:
First: just the digits (with the decimal point placed after the first digit),
Followed by: ×10 to a power that will put the decimal point back where it should be.

4. Explain how to convert from Scientific Notation to Decimal Notation, and give an example.
A number in scientific notation is written as the product of a number (integer or decimal) and a power of 10.
The number has one digit to the left of the decimal point. The power of ten indicates how many places the decimal point was moved. Look at the exponet of 10 and move your decimal to its orginal place. Ex: The number 6.5x10-7 written in decimal format would be 0.00000065 because the decimal point was moved 7 places to the left to form the decimal 0.00000065.

5. Explain how to convert from Decimal Notation to Scientific Notation, and give an example.
Scientific notation is used to express very large or very small numbers. A number in scientific notation is written as the product of a number (integer or decimal) and a power of 10. The number has one digit to the left of the decimal point. The power of ten indicates how many places the decimal point was moved.
The decimal number 0.00000065 written in scientific notation would be 6.5x10-7 because the decimal point was moved 7 places to the right to form the number 6.5. It is equivalent to 6.5*0.1*0.1*0.1*0.1*0.1*0.1*0.1

6. Explain how to multiple scientific notation numbers, and give an example.
To multiply two numbers expressed in scientific notation, simply multiply the numbers out front and add the exponents. : (n x 10a) • (m x 10b) = (n · m) x 10a+b

7. Explain how to divide scientific notation numbers, and give an example.
To divide two numbers expressed in scientific notation, simply divide the numbers out front and subtract the exponents. n*10^a/m*10^b= n/m 10^(a-b)

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