Exponents

Question 1

Variable with an even exponent

Answer 1

Has 2 solutions…(negative and positive)

Question 2

Distribution shortcut

Answer 2

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

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

Question 3

Raising powers to a power

Answer 3

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)

Question 4

Multiplication and division - same base

Answer 4

Add the exponents

3^4 * 3^3 = 3^7

Multiply the coefficients, but do not change the base.
5n^4 * 5n^4 = 25n^6

Question 5

To divide terms with SAME BASE

Answer 5

..subtract their exponents

Question 6

Negative exponents..”flip the base”

Answer 6

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

Question 7

Any term raised to 0…

Answer 7

…equals 1, except for 0 itself.

Question 8

Addition and subtraction of exponents

Answer 8

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)

Question 9

Difference between squares (x^2 - y^2)

Answer 9

Special sort of factoring
(x^2 - y^2) = (x+y)(x-y)
17^2 - 13^2 = (17+13)(17-13) = 30(4) = 120

Question 10

Multiplying and dividing - same exponents (different base)

Answer 10

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

Question 11

Break down the bases

Answer 11

…break down the bases to their prime factors.

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

Question 12

Exponent equations

2^(2x-1) = 16

Answer 12

1. Make the bases the same
2. Set the exponents equal
3. Solve for x