Flashcards in Exponents Deck (12):
Variable with an even exponent
Has 2 solutions...(negative and positive)
(3n)^4=3^4 x n^4 = 81n^4
[ONLY WORKS FOR SIMPLE EXPRESSIONS - i.e., with no addition or subtraction]
Raising powers to a power
Multiply the the exponents (when working with SIMPLE expressions, be sure to distribute the outside exponent to EVERY term in the expression; when working with COMPLEX expressions, must combine the terms in the parenthesis before multiplying the exponents)
Multiplication and division - same base
Add the exponents
3^4 * 3^3 = 3^7
Multiply the coefficients, but do not change the base.
5n^4 * 5n^4 = 25n^6
To divide terms with SAME BASE
..subtract their exponents
Negative exponents.."flip the base"
Negative exponent tells us how many times to divide by something. 3^-1 = 1/3. N
You can make any exponent positive by taking the reciprocal of its base
Any term raised to 0...
...equals 1, except for 0 itself.
Addition and subtraction of exponents
1. What is the largest element in common to all of the terms?
2. What do I have to multiply with that common element to recreate the original expression?
12n^3 + 4n^2 + 8n
4n(3n^2 + n + 2)
Difference between squares (x^2 - y^2)
Special sort of factoring
(x^2 - y^2) = (x+y)(x-y)
17^2 - 13^2 = (17+13)(17-13) = 30(4) = 120
Multiplying and dividing - same exponents (different base)
Multiply/divide the base!
2^4 * 10^4 = 20^4
n^8 * p^8 = (np)^8
10^4/2^4 = 5^4
X^3/y^3 = (x/y)^3
Break down the bases
...break down the bases to their prime factors.
15^25 = (3*5)^25 = 3^25 *5^25