# Exponents Flashcards

1
Q

-3² Equals

A

9

2
Q

Product Rule

r s r + s
Y × Y = Y

Exp.

Y³ × Y⁵ =

A

Y⁸

3
Q

Quotient Rule

r
Y            r - s
---------- = Y
s
Y

Exp.

6
A
----------- =
2
A
A

4

A

4
Q

Power of Product
2 2 2
(x . y) = x . y

Exp.
2
(a.b) =

A

2 2

a . b

5
Q

Power of Power
r s rs
( x ) = x

Exp.
2 5
( z )

A

10

z

6
Q

Power of quotient

r       r     r ( x/y)   = x /  y

Exp.
3
(5/7) =

A

3 3

5 / 7

7
Q

Negative exponent
-r r
x = 1/ x

Exp.
-6
b =

A

1/ b⁶

8
Q

Zero exponent

0
X =1 , if x ≠ 0

Exp
0
7 =

A

1

9
Q

Negative exponent with a quotient
- r r
( x / y ) = (y/x)

Exp.
-3
( 1/2) =

Or
-2
5 =

A

3
(2/1) or 2³

-2 -2 2
5 = (5/1) = (1/5)

10
Q

Describe what this equals in Simple terms
-3
2

A

It equals 1÷2÷2÷2 = 0.125

Or

1/8 = 0.125

11
Q

Law of exponent of 1
1 1 1
X = , 4 =, 79 =

A

X, 4, 79

12
Q

Law of exponent of 0
0 0 0
X = , 25 = , 444 =

A

1, 1, 1

13
Q

Law of Negative exponents in simple terms
-n
Give solución x

A

The negative interger is divided by 1

n     1/ x

It is x to the positive n power

14
Q

(4²)³

A

4⁶

15
Q

(x⁴ × y² × z³)⁴

A

x¹⁶× y⁸×z¹²

16
Q

(2 x y³)²

A

2² x² y⁶ = 4 x² y⁶

17
Q

(2x + 3)²

What method do we use to solve when there is a plus or minus sign inside the parentheses and raised to an exponent

A

Foil

(2x + 3) (2x + 3)

4x² + 12x + 9

18
Q

(2x + 3)²

What method do we use to solve when there is a plus or minus sign inside the parentheses and raised to an exponent

A

Foil

2x + 3) (2x + 3

19
Q

Y⁴ × Y⁵ =

A

Y⁹

20
Q

( x³)⁴

A

x¹²

21
Q

( X to negative 3)

Negative 3
X =

How to “Solve this Problem”

A

= 1 / X³

22
Q

1
—–
-4
X

How to Simplify

A

X
_____

1
23
Q

Y ⁵ × Y ² =

A

Y ⁷

24
Q

X⁷/ X³ =

A

X⁴

25
Q

(X³)⁴

A

X¹²

26
Q

X⁰

A

1

27
Q

X (‐³) “Raised to negative 3”

A

1/ x³

Make it positive and put it under 1

28
Q

1 / x -⁴

A

X⁴

Take away signs on negatives and flip sides

29
Q

2. (-3)²

A
1. -9

2. 9

30
Q

Y⁴ × Y -⁹ =

A

1 / x⁵

31
Q

(X³) -⁵ =

A

X-¹⁵ = 1/ x¹⁵

32
Q

X⁷/ X¹² =

A

X-⁵ = 1/ x⁵

33
Q

(-2x³y⁴)² Simplify

A

(-2)² (x⁶y⁸)

4 x⁶y⁸

34
Q

(5x³) (4x⁷) Simplify

A

20 x¹⁰

Why not FOIL it?

Because there is no plus or minus symbol in it.

35
Q

(7x⁶) (5x⁴)

A

35 x¹⁰

36
Q

(4x³y²) (7x-⁴y³)

A

28x-¹y⁵ = 28y⁵/ x

37
Q

(-2x³y)⁰

A

1

38
Q

-4x⁰

A

-4 (x)⁰ = -4 (1) = -4

39
Q

24x⁷y³/ 8x⁴y-¹² =

A

3x³y¹⁵

40
Q

( 35x³y⁵/ 63x-⁴y⁷ ) ²

A

You can simplify or distribute first

(5x⁷/9y²)² = 25 x¹⁴/ 81 y⁴

41
Q

(3/4) -² how to get rid of negative exponent

A

(4/3)² = 16/9

42
Q

(X³) -⁴

A

= x-¹²/ 1 = 1/x¹²

43
Q

(4x-⁵)²

A

= 4²x-¹⁰ = 16/ x¹⁰

44
Q

Y⁵/ Y -³

A

Y⁸

45
Q

X-⁸/X-¹¹ =

A

46
Q

5 - 2 (x-³y⁴)⁰

A

5 - 2×(1) = 3

47
Q

3a-⁴
————
b-⁶ c³

A

3 b⁶
———
a⁴ c³

48
Q

(3 x-²y³)² (4x⁵y-⁶)

A

3² x-⁴y⁶ 4³x¹⁵y‐¹⁸

9 × 16 x¹¹ y‐¹² =

576x¹¹/ y¹²

49
Q

45 x⁴ y-⁶ / 27x-⁷y⁵

A

5x¹¹ / 3y¹¹

50
Q

18 a³b-⁴c-⁶ / 30a⁷b⁵c-⁹

A

3c³ / 5a⁴b⁹

51
Q

(63x-³y⁴z-⁵ / 35x⁸y-⁷z-⁴)²

A

81y²²/ 25x²²z²