When multiplying expression with the same base, we keep the base and add the exponents.
x4*x3 = x4+.3= x7
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.
x5/x3 = x*x*x*x*x*/x*x*x* = 1x2/1 = x2
Zero Exponent Rule
Any real number, except 0, raised to the zero power equals 1. 30= 1 x0 = 1
Power Rule for Exponents
When we raise and exponential expression to a power, we keep the base and multiply the exponents. (x3)2= x3*2 = x5
Expanded Power Rule
Every factor within parentheses is raised to the power outside the parentheses when the expression is simplified.
(ax/by)2 = a2x2/b2y2
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.
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*104
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 100since it equals 1. This will result in a number greater than or equal to 1 but less than 10.
Calculations Using Scientific Notations
To add or subtract numbers in scientific notation, we generally make the exponents on the 10's the same. 8.3x104- 1.02x105= 8.3x104-10.2x104
an expression containing the sum of a finite number of terms of the form axn , for any real number a and any whole number n. Examples: 8x, 1/3x-4, x2-2x+1 Not Polynomial: 4x1/2, 3x2+4x-1+5, (neg exponent) 4+1/x (1/x=x-1, negative exponent)
Types of Polynomial
Monomial: Polynomial with one term Binomial : two-termed polynomial Trinomial: three-termed polynomial
Degree of a Term
The degree of a term of a polynomial in one variable is the exponent on the variable in that term. 4x2Second 2y5 Fifth -5x First 3 Zero
Degree of a polynomial
I the same as that of its highest-degree term 8x3+2x2-3x+4 Third (8x3is the highest-degree term) x2-4 Second (x2is highest-degree term) 6x-5 First (6x 6x1 is the highest degree-term) 4 Zero x2y4+2x+3 Sixth (x2y4is the highest-degree term)
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.
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
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.
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