Flashcards in Exponents and Roots Deck (19)

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1

## 0^0

###
Undefined

B/c could be 1 * 0 zero times so your left with 1.

OR

Could be zero

2

##

a^n

###

means one times n a’s.

Where n is a non-negative number

3

## Negative number to an even exponent

### Positive

4

## Negative number to an odd exponent

### Negative

5

## Exponents of decimals

### Remember that the final answer’s number of decimals (past the decimal point) is the sum of all decimal places of the elements being multiplied.

6

## Principal Root

###
Positive Square root only

Else: +- symbol in front of sqrt

7

## x ² = 9

### x = 3, x = -3

8

## What does it mean to simplify a square root?

### It means find the perfect squares to remove from under the square root sign.

9

## sqrt(1 / 200)

###
= sqrt(1) / sqrt(200)

= 1 / 10sqrt(2)

10

## a^-x

### = 1/a^x

11

## (a/b)^-x

### (b/a)^x

12

## (1/2)^-2

### 2^2 = 4

13

## (2/4)^-2

###
(4/2)^2

(16/4) = 4

14

## Adding and subtracting radicals

###
Must have like radicands

(Expression under the root)

Only operate on the numbers in front of the radicals

15

## Multiply radicals

###
Must have same index number

3root(x) * 3root(y) = 3root(xy)

Same law as multiplying polynomials:

In general, when multiplying two polynomials together, use the distributive property, until every term of one polynomial is multiplied times every term of the other polynomial. Make sure that you simplify your answer by combining any like terms.

16

## Divide radicals

###
A Quotient of Two Radicals

With the Same Index Number

If n is even, x and y represent any nonnegative real number

and y does not equal 0.

If n is odd, x and y represent any real number and y does not equal 0.

nroot(x) / nsqrt(y) = nroot(x / y)

17

## Roots of variables with exponents

###
Divide exponents by index and sum for new variable exponent combo left of radical.

Remainder goes back under the radical as the exponent of the radicand

eg:

Sqrt(z^7) = z^3 sqrt(z)

18

## Raising an exponent to a power

###
Multiply the exponents, keep base!

** Must have the same base and same index!!

(Z^3)^2 x Z = Z^7

2^2 x 2^3 = 2^5 = 32

19