Exponents

Question 1

-3² Equals

Answer 1

9

Question 2

Product Rule

r s r + s
Y × Y = Y

Exp.

Y³ × Y⁵ =

Answer 2

Y⁸

Question 3

Quotient Rule

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

Exp.

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

Answer 3

4

A

Question 4

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

Exp.
2
(a.b) =

Answer 4

2 2

a . b

Question 5

Power of Power
r s rs
( x ) = x

Exp.
2 5
( z )

Answer 5

10

z

Question 6

Power of quotient

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

Exp.
3
(5/7) =

Answer 6

3 3

5 / 7

Question 7

Negative exponent
-r r
x = 1/ x

Exp.
-6
b =

Answer 7

1/ b⁶

Question 8

Zero exponent

0
X =1 , if x ≠ 0

Exp
0
7 =

Answer 8

1

Question 9

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

Exp.
-3
( 1/2) =

Or
-2
5 =

Answer 9

3
(2/1) or 2³

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

Question 10

Describe what this equals in Simple terms
-3
2

Answer 10

It equals 1÷2÷2÷2 = 0.125

Or

1/8 = 0.125

Question 11

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

Answer 11

X, 4, 79

Question 12

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

Answer 12

1, 1, 1

Question 13

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

Answer 13

The negative interger is divided by 1

      n     1/ x

It is x to the positive n power

Question 14

(4²)³

Answer 14

4⁶

Question 15

(x⁴ × y² × z³)⁴

Answer 15

x¹⁶× y⁸×z¹²

Question 16

(2 x y³)²

Answer 16

2² x² y⁶ = 4 x² y⁶

Question 17

(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

Answer 17

Foil

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

4x² + 12x + 9

Question 18

(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

Answer 18

Foil

2x + 3) (2x + 3

Question 19

Y⁴ × Y⁵ =

Answer 19

Y⁹

Question 20

( x³)⁴

Answer 20

x¹²

Question 21

( X to negative 3)

Negative 3
X =

How to “Solve this Problem”

Answer 21

= 1 / X³

Question 22

1
—–
-4
X

How to Simplify

Answer 22

⁴
X
_____

                         1

Question 23

Y ⁵ × Y ² =

Answer 23

Y ⁷

Question 24

X⁷/ X³ =

Answer 24

X⁴

Question 25

(X³)⁴

Answer 25

X¹²

Question 26

X⁰

Answer 26

1

Question 27

X (‐³) “Raised to negative 3”

Answer 27

1/ x³

Make it positive and put it under 1

Question 28

1 / x -⁴

Answer 28

X⁴

Take away signs on negatives and flip sides

Question 29

1. • 3²

2. (-3)²

Answer 29

1. -9

2. 9

Question 30

Y⁴ × Y -⁹ =

Answer 30

1 / x⁵

Question 31

(X³) -⁵ =

Answer 31

X-¹⁵ = 1/ x¹⁵

Question 32

X⁷/ X¹² =

Answer 32

X-⁵ = 1/ x⁵

Question 33

(-2x³y⁴)² Simplify

Answer 33

(-2)² (x⁶y⁸)

4 x⁶y⁸

Question 34

(5x³) (4x⁷) Simplify

Answer 34

20 x¹⁰

Why not FOIL it?

Because there is no plus or minus symbol in it.

Question 35

(7x⁶) (5x⁴)

Answer 35

35 x¹⁰

Question 36

(4x³y²) (7x-⁴y³)

Answer 36

28x-¹y⁵ = 28y⁵/ x

Question 37

(-2x³y)⁰

Answer 37

1

Question 38

-4x⁰

Answer 38

-4 (x)⁰ = -4 (1) = -4

Question 39

24x⁷y³/ 8x⁴y-¹² =

Answer 39

3x³y¹⁵

Question 40

( 35x³y⁵/ 63x-⁴y⁷ ) ²

Answer 40

You can simplify or distribute first

(5x⁷/9y²)² = 25 x¹⁴/ 81 y⁴

Question 41

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

Answer 41

(4/3)² = 16/9

Question 42

(X³) -⁴

Answer 42

= x-¹²/ 1 = 1/x¹²

Question 43

(4x-⁵)²

Answer 43

= 4²x-¹⁰ = 16/ x¹⁰

Question 44

Y⁵/ Y -³

Answer 44

Y⁸

Question 45

X-⁸/X-¹¹ =

Answer 45

X³

Question 46

5 - 2 (x-³y⁴)⁰

Answer 46

5 - 2×(1) = 3

Question 47

3a-⁴
————
b-⁶ c³

Answer 47

3 b⁶
———
a⁴ c³

Question 48

(3 x-²y³)² (4x⁵y-⁶)

Answer 48

3² x-⁴y⁶ 4³x¹⁵y‐¹⁸

9 × 16 x¹¹ y‐¹² =

576x¹¹/ y¹²

Question 49

45 x⁴ y-⁶ / 27x-⁷y⁵

Answer 49

5x¹¹ / 3y¹¹

Question 50

18 a³b-⁴c-⁶ / 30a⁷b⁵c-⁹

Answer 50

3c³ / 5a⁴b⁹

Question 51

(63x-³y⁴z-⁵ / 35x⁸y-⁷z-⁴)²

Answer 51

81y²²/ 25x²²z²