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Exponent Rules > Exponent Rules And Problem Examples > Flashcards

Exponent Rules And Problem Examples Flashcards

1
Q

What is

The Product Rule

A

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

^ = exponent, * = times

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2
Q

What is

The Quotient Rule

A

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

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3
Q

What is

The Power Rule

A

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

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4
Q

What is

The Power of Zero

A

x^0 = 1

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5
Q

What is

Negative Exponent

A

X^-n = 1 / x^n

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6
Q

What is

Fractional Exponent

A

x^1/n = n√x

√ = Root

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7
Q

What is

Distribute Exponent Over a Product

A

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

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8
Q

What is

Distribute Exponent Over a Quotient

A

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

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9
Q

What rule is

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

A

The Product Rule

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10
Q

What Rule is

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

A

The Quotient Rule

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11
Q

What rule is

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

A

The Power Rule

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12
Q

What rule is

x^0 = 1

A

The Power of Zero

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13
Q

What rule is

X^-n = 1 / x^n

A

Negative Exponent

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14
Q

What rule is

x^1/n = n√x

A

Fractional Exponent

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15
Q

What rule is

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

A

Distribute Exponent Over a Product

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16
Q

What rule is

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

A

Distribute Exponent Over a Quotient

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17
Q

Simplify this without writing negative exponents

3x^-2 / x^4

A

3 / x^6

Detailed Explanation

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

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18
Q

Simplify this without writing negative exponents

4y^3 / y^-5

A

4y^8

Detailed Explanation

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

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19
Q

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

A

z^7 / 7y^4

Detailed Explanation

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

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20
Q

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

A

5^3 * x^15 / y^12

Detailed Explanation

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

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21
Q

Evalute the expression: Question a

(-3)^4

Where I got the problems

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

A

81

In here -3 is the base

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22
Q

Question b

-3^4

A

-81

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

So 81 time negative = -81

23
Q

Question c

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

A

-1/8

23
Q

Question d

(-2)^5

A

-32

24
Q

Question e

-2^5

A

-32

25
Q

Question f

(-6)^2 * (1/6)^2

A

1

26
Q

Question g

(2/5)^0 * (3)^-1

A

1/3

27
Q

Question h

3^-2 / 5^0

A

1/9

28
Q

Question i

(-2/5)^-2

A

25/4 = 6 + 1/4

29
Q

Question j

5^2 * 5

A

125

30
Q

Question k

5^8 * 5^-6

A

25

31
Q

Question l

5^-8 * 5^6

A

1/25

32
Q

Question m

(2^3)^2

A

2^6 = 64

33
Q

Question n

10^8 / 10^5

A

10^3 = 1000

34
Q

Question o

10^2 / 10^-2

A

10^4 = 10000

35
Q

Simplify each expression and eliminate negative exponents.

x^5 * x^8

A

x^13

36
Q

(2x^3)^2

A

4 * x^6

37
Q

x^-3 * x^5

A

x^2

38
Q

y^6 * y^9

A

y^15

39
Q

y^7 * y^-3

A

y^4

39
Q

(3x)^3

A

27 * x^3

40
Q

z^-8 * z^3

A

1 / z^5

41
Q

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

A

1 / x^4

42
Q

x^15 / x^10

A

x^5

43
Q

y^3 * y^-9

A

1 / y^6

44
Q

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

A

w

45
Q

x^8 * x^0 / x^12

x^8 times x^0 over x^12

A

1 / x^4

46
Q

b^8 * b^-3 / b

A

b^4

47
Q

(z^3 * z^5)^2

A

z^16

48
Q

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

A

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

49
Q

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

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

A

y^9

50
Q

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

A

-8 * b^18

51
Q

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

A

72 / x^2

Exponent Rules (1 decks)

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