Exponents

Question 1

Base

2y^3

Answer 1

y

Question 2

Coefficient

2y^3

Answer 2

2

Question 3

Exponent

2y^3

Answer 3

3

Question 4

Rule 1: Addition and Subtraction

Answer 4

If

Same base
Same exponent

then Add or Subtract the COEFFICIENT

4^3 + 4^3 + 4^3 + 4^3 = 4(4^3)
x^2 + x^2 = 2x^2

7(4^3) + 2(4^4) = NO!

You’re not changing the base, you’re changing the coefficient

2^29 - 2^28 = 2^28

Question 5

Rule 2a: Multiplication

Same bases

Answer 5

ADD EXPONENTS
2y^4 X 4y^4 = 8x^8

Multiply coefficients

Question 6

Rule 3a: Division

same bases

Answer 6

SUBTRACT exponents

divide coefficients

Question 7

Rule 3b: Division

same exponent

Answer 7

divide bases

divide coefficients

Question 8

Rule 3c: Division

same base
same exponent

Answer 8

quotient of coefficient +1

Question 9

Rule 2b: Multiplication

same exponents

Answer 9

Multiply bases
7y^5 x 3y^5 = 21(y^2)^5
and multiply coefficients

Question 10

Rule 2c: Multiplication

same base and same exponent

Answer 10

add exponents or multiply bases,

AND multiple coefficients

Question 11

Rule 4a: Negative exponents

for terms with negative exponent in numerator

Answer 11

flip the base to denominator
make exponent positive

leave coefficient unflipped

Question 12

Rule 4b: Negative exponents

if negative exponent is in denominator

Answer 12

flip just base into the numerator

leave coefficients unflipped

1 / 2x^-4 = x^4 / 2

Question 13

Rule 5a: The powers of one and zero

any term to the first power

Answer 13

equals itself

Question 14

Rule 5b: The powers of one and zero

any term to the zero power

Answer 14

has a value of 1

unless it’s zero, which is undefined

Question 15

Rule 6a: resolving parentheses

exponents outside parentheses of a simple expression (no addition or subtraction within parentheses)

Answer 15

distribute exponent outside the parentheses to each term within the parentheses

(-2z)^-x = (-2)^-x, z^-x = 1 / (-2)^x, z^x

Question 16

Rule 6b: resolving parentheses

for exponents outside parentheses of a complex expression (addition/subtraction within parentheses)

Answer 16

combine terms within parentheses and distribute the exponent
(2+3)^4 = (5)^4 = 625

if terms within parentheses cannot be combined, exponent cannot be distributed
(x+y)^2 = (x+y)(x+y)
NOT: x^2 + y^2

Question 17

Rule 7a: Consecutive Exponents

expression w/ exponents inside and outside parentheses

Answer 17

multiply exponents

(4^x)^x = 4^x^2

Question 18

Rule 7b: Consecutive Exponents

simple expressions
with exponents in parentheses and outside parentheses

Answer 18

distribute the outside exponent to every term within the expression

(2z^x)^y = 2^y, z^xy

Question 19

Rule 7c: Consecutive Exponents

complex expressions
with exponents inside and outside parentheses

Answer 19

combine terms within parentheses
THEN
multiply the exponents

(3z^4 - z^4)^3=
(2z^4)^3 =
(2^3, z^12) =
8z^12

if terms within complex expression cannot be combined, the expression must be multiplied out in its entirety
(x^2 + y^2)^2 =
(x^2+y^2) + (x^2+y^2)
NOT: = x^4+y^4

Question 20

Rule 8: Fractional exponent

Answer 20

1. denominator of fractional exponent: becomes the root to take of the original base
2. numerator of fractional exponent: becomes the power to which the NEW base should be raised

27 ^2/3 = 9

Question 21

Rule 2d: Multiplication

coefficients with different bases and different exponents

Answer 21

coefficients with DIFFERENT bases should be multiplied, though can’t do anything else with them for multiplication problem

Question 22

Rule 3d: division

different bases, different exponents

Answer 22

divide coefficients

Question 23

rule 5c: powers of one and zero

anything divided by 0

Answer 23

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