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Algebra Review > Exponents and Roots > Flashcards

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

Multiplying exponents

Add 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