Exponent Rules And Problem Examples

Question 1

What is

The Product Rule

Answer 1

x^n * x^m = x^n+m

^ = exponent, * = times

Question 2

What is

The Quotient Rule

Answer 2

x^n / x^m = x^n-m

Question 3

What is

The Power Rule

Answer 3

(x^n)^m = x^n*m

Question 4

What is

The Power of Zero

Answer 4

x^0 = 1

Question 5

What is

Negative Exponent

Answer 5

X^-n = 1 / x^n

Question 6

What is

Fractional Exponent

Answer 6

x^1/n = n√x

√ = Root

Question 7

What is

Distribute Exponent Over a Product

Answer 7

(x * y)^n = x^n * y^n

Question 8

What is

Distribute Exponent Over a Quotient

Answer 8

(x/y)^n = x^n / y^n

Question 9

What rule is

x^n * x^m = x^n+m

Answer 9

The Product Rule

Question 10

What Rule is

x^n / x^m = x^n-m

Answer 10

The Quotient Rule

Question 11

What rule is

(x^n)^m = x^n * m

Answer 11

The Power Rule

Question 12

What rule is

x^0 = 1

Answer 12

The Power of Zero

Question 13

What rule is

X^-n = 1 / x^n

Answer 13

Negative Exponent

Question 14

What rule is

x^1/n = n√x

Answer 14

Fractional Exponent

Question 15

What rule is

(x * y)^n = x^n * y^n

Answer 15

Distribute Exponent Over a Product

Question 16

What rule is

(x/y)^n = x^n / y^n

Answer 16

Distribute Exponent Over a Quotient

Question 17

Simplify this without writing negative exponents

3x^-2 / x^4

Answer 17

3 / x^6

Detailed Explanation

https://youtu.be/LwCRRUa8yTU?list=PLd1rKQgU40fhukHTOuUFZVYcYFyys4Abk&t=711

Question 18

Simplify this without writing negative exponents

4y^3 / y^-5

Answer 18

4y^8

Detailed Explanation

https://youtu.be/LwCRRUa8yTU?list=PLd1rKQgU40fhukHTOuUFZVYcYFyys4Abk&t=837

Question 19

Simplify this without writing negative exponents

y^3 * z^5 / 7z^-2 * y^7

y^3 times z^5 over 7 times z^-2 times y^7

Answer 19

z^7 / 7y^4

Detailed Explanation

https://youtu.be/LwCRRUa8yTU?list=PLd1rKQgU40fhukHTOuUFZVYcYFyys4Abk&t=1017

Question 20

Simplify this without writing negative exponents

(25x^4 * y^-5 / x^-6 * y^3)^3/2

(25 times x^4 times y^-5 over x^-6 times y^3) ^ 3 over 2

Answer 20

5^3 * x^15 / y^12

Detailed Explanation

https://youtu.be/LwCRRUa8yTU?list=PLd1rKQgU40fhukHTOuUFZVYcYFyys4Abk&t=1099

Question 21

Evalute the expression: Question a

(-3)^4

Where I got the problems

https://www.uwinnipeg.ca/mathstats/docs/Exponents%20and%20radicals.pdf

Answer 21

81

In here -3 is the base

Question 22

Question b

-3^4

Answer 22

-81

In here 3 is the base and then you multiply 81 with the negative

So 81 time negative = -81

Question 23

Question c

(1/8)^2 * (-2)^3

Answer 23

-1/8

Question 23

Question d

(-2)^5

Answer 23

-32

Question 24

# Question e -2^5

Answer 24

-32

Question 25

# Question f (-6)^2 * (1/6)^2

Answer 25

1

Question 26

# Question g (2/5)^0 * (3)^-1

Answer 26

1/3

Question 27

# Question h 3^-2 / 5^0

Answer 27

1/9

Question 28

# Question i (-2/5)^-2

Answer 28

25/4 = 6 + 1/4

Question 29

# Question j 5^2 * 5

Answer 29

125

Question 30

# Question k 5^8 * 5^-6

Answer 30

25

Question 31

# Question l 5^-8 * 5^6

Answer 31

1/25

Question 32

# Question m (2^3)^2

Answer 32

2^6 = 64

Question 33

# Question n 10^8 / 10^5

Answer 33

10^3 = 1000

Question 34

# Question o 10^2 / 10^-2

Answer 34

10^4 = 10000

Question 35

# Simplify each expression and eliminate negative exponents. x^5 * x^8

Answer 35

x^13

Question 36

(2x^3)^2

Answer 36

4 * x^6

Question 37

x^-3 * x^5

Answer 37

x^2

Question 38

y^6 * y^9

Answer 38

y^15

Question 39

y^7 * y^-3

Answer 39

y^4

Question 39

(3x)^3

Answer 39

27 * x^3

Question 40

z^-8 * z^3

Answer 40

1 / z^5

Question 41

x^-2 * x^-6 * x^4

Answer 41

1 / x^4

Question 42

x^15 / x^10

Answer 42

x^5

Question 43

y^3 * y^-9

Answer 43

1 / y^6

Question 44

w^5 * w^-8 * w^4

Answer 44

w

Question 45

x^8 * x^0 / x^12 | x^8 times x^0 over x^12

Answer 45

1 / x^4

Question 46

b^8 * b^-3 / b

Answer 46

b^4

Question 47

(z^3 * z^5)^2

Answer 47

z^16

Question 48

(3x^4) (x/3)^3

Answer 48

3x^7 / 27 = x^7 / 9

Question 49

y^3 * y^5 / y^2 * y^-3 | y^3 times y^5 over y^2 times y^-3

Answer 49

y^9

Question 50

(-2b^3 * b^3)^3

Answer 50

-8 * b^18

Question 51

(-3x^2)^2 * (2x^-2)^3

Answer 51

72 / x^2