- StudyBlue
- Wisconsin
- University of Wisconsin - Madison
- Mathematics
- Mathematics 091
- Harrison
- Chapter 4

Betty-Anne W.

Product Rule for Exponents

When multiplying expression with the same base, we keep the base and add the exponents.

x^{4}*x^{3} = x^{4+.3}= x^{7}

x

Quotients Rule for Exponents

When dividing expressions with the same base, __keep the base __and subtract the exponents in the denominator from the exponents in the numerator.

x^{5}/x^{3} = x*x*x*x*x*/x*x*x* = 1x^{2}/1 = x^{2}

Pg 234a

x

Pg 234a

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Zero Exponent Rule

Any real number, except 0, raised to the zero power equals 1.

3^{0}= 1

x^{0} = 1

3

x

Power Rule for Exponents

When we raise and exponential expression to a power, we keep the base and multiply the exponents.

(x^{3})^{2}= x^{3*2} = x^{5}

(x

Expanded Power Rule

Every factor within parentheses is raised to the power outside the parentheses when the expression is simplified.

(ax/by)^{2} = a^{2}x^{2}/b^{2}y^{2}

(ax/by)

Negative Exponent Rule

When a variable or number is raised to a negative exponent, the expression may be rewritten as 1 divided by the variable or number raised to that positive exponent.

x^{-2}= 1/x^{2}

x

Write a Number in Scientific Notation

1) Move the decimal point in the original number to the right of the first nonzero digit. This will give a number greater than or equal to 1 and less than 10.

Multiply the number obtained in step 1 by 10 raised to the count(power) .

18,500 = 1.85*10^{4}

Multiply the number obtained in step 1 by 10 raised to the count(power) .

18,500 = 1.85*10

Covert a Number from Scientific Notation to Decimal

If the exponent is positive, move the decimal point in the number to the right.

If the exponent is negative, move the decimal point in the number to the left.

If the exponent is 0, do not move the decimal point. Drop the factor 10^{0}since it equals 1. This will result in a number greater than or equal to 1 but less than 10.

If the exponent is negative, move the decimal point in the number to the left.

If the exponent is 0, do not move the decimal point. Drop the factor 10

Calculations Using Scientific Notations

To add or subtract numbers in scientific notation, we generally make the exponents on the 10's the same.

8.3x10^{4}- 1.02x10^{5}= 8.3x10^{4}-10.2x10^{4}

8.3x10

Identify Polynomial

an expression containing the sum of a finite number of terms of the form ax^{n} , for any real number a and any **whole number** n.

Examples: 8x, 1/3x-4, x^{2}-2x+1

Not Polynomial: 4x^{1/2}, 3x^{2}+4x^{-1}+5, (neg exponent) 4+1/x (1/x=x^{-1}, negative exponent)

Examples: 8x, 1/3x-4, x

Not Polynomial: 4x

Types of Polynomial

Monomial: Polynomial with one term

Binomial : two-termed polynomial

Trinomial: three-termed polynomial

Binomial : two-termed polynomial

Trinomial: three-termed polynomial

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Degree of a Term

The degree of a term of a polynomial in one variable is the exponent on the variable in that term.

4x^{2}Second

2y^{5} Fifth

-5x First

3 Zero

4x

2y

-5x First

3 Zero

Degree of a polynomial

I the same as that of its highest-degree term

8x^{3}+2x^{2}-3x+4 Third (8x^{3}is the highest-degree term)

x^{2}-4 Second (x^{2}is highest-degree term)

6x-5 First (6x 6x^{1 }is the highest degree-term)

4 Zero

x^{2}y^{4}+2x+3 Sixth (x^{2}y^{4}is the highest-degree term)

8x

x

6x-5 First (6x 6x

4 Zero

x

Add Polynomials

Combine like terms

Add Polynomials in Columns

1) Arrange polynomials in descending order, one under the other with like terms in the same columns.

2) Add the terms in each column.

pg 263

2) Add the terms in each column.

pg 263

Subtract Polynomials

1) Use the distributive property to remove parentheses ( this will have the effect of changing the sign of **every** term within the parentheses of the polynomial **being subtracted**.)

2) Combine like terms

2) Combine like terms

Subtract Polynomials in Columns

1)Write the polynomial being subtracted below the polynomial from which it is being subtracted. List like terms in the same column.

2) Change the sign of each term in the polynomial being subtracted. (This step can be done mentally, if you like)

3) Add the terms in each column.

2) Change the sign of each term in the polynomial being subtracted. (This step can be done mentally, if you like)

3) Add the terms in each column.

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