Flashcards in Exponents Deck (12)

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1

## Variable with an even exponent

### Has 2 solutions...(negative and positive)

2

## Distribution shortcut

###
(3n)^4=3^4 x n^4 = 81n^4

[ONLY WORKS FOR SIMPLE EXPRESSIONS - i.e., with no addition or subtraction]

3

## 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)

4

## 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

5

## To divide terms with SAME BASE

### ..subtract their exponents

6

## 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

7

## Any term raised to 0...

### ...equals 1, except for 0 itself.

8

## Addition and subtraction of exponents

###
FACTOR

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)

9

## 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

10

## 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

11

## Break down the bases

###
...break down the bases to their prime factors.

15^25 = (3*5)^25 = 3^25 *5^25

12