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pre calc > roots and powers > Flashcards

roots and powers Flashcards

1
Q

What is the definition of a square root?

A

A square root of a number is a value that, when multiplied by itself, gives the original number.

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2
Q

True or False: The square root of a negative number is a real number.

A

False

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3
Q

What is the symbol for square root?

A

The symbol for square root is √.

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4
Q

Fill in the blank: The square root of 16 is ____.

A

4

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5
Q

What is the cube root of 27?

A

3

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6
Q

True or False: The cube root of a negative number is always negative.

A

True

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7
Q

What is the exponent in the expression 2^5?

A

5

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8
Q

What is the base in the expression 3^4?

A

3

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9
Q

Fill in the blank: 5 to the power of 0 equals ____.

A

1

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10
Q

If a^m * a^n = a^?, what is the answer?

A

m + n

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11
Q

What is the result of (2^3) * (2^2)?

A

2^5 or 32

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12
Q

What is the value of 10^(-2)?

A

0.01

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13
Q

What is the product of 3^2 and 3^3?

A

3^5 or 243

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14
Q

True or False: The fourth root of 81 is 3.

A

True

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15
Q

What does it mean when we say a number is raised to a negative exponent?

A

It means to take the reciprocal of the number raised to the positive exponent.

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16
Q

Fill in the blank: The cube root of x^3 is ____.

A

x

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17
Q

What is the value of √(x^2)?

A

|x|

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18
Q

What is the term for a number raised to the power of one?

A

Identity

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19
Q

If x = 4, what is x^2?

A

16

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20
Q

What is the result of 2^3 + 2^3?

A

16

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21
Q

What is the expression for the nth root of a number?

A

The nth root of a number a is expressed as a^(1/n).

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22
Q

True or False: The square of a negative number is negative.

A

False

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23
Q

Fill in the blank: The expression 9^(1/2) equals ____.

A

3

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24
Q

What is the value of (x^4)^(1/2)?

25
What is the result of 5^3?
125
26
If a = 2 and b = 3, what is a^b?
8
27
What is the value of -3^2?
9
28
What is the definition of a power?
A power is a number that is expressed as a base raised to an exponent.
29
Fill in the blank: The expression (x^3)(x^2) simplifies to ____.
x^5
30
What is the result of (4^2)/(4^3)?
4^(-1) or 1/4
31
True or False: The square root of 25 is 5.
True
32
What is the value of 7^0?
1
33
If x = 2, what is x^4?
16
34
What is the term for a number that is multiplied by itself?
Square
35
Fill in the blank: The square root of 49 is ____.
7
36
What is the relationship between exponents and roots?
Roots can be expressed as fractional exponents.
37
What is the value of (2^4) / (2^2)?
2^2 or 4
38
Fill in the blank: The expression a^(1/n) represents ____.
The nth root of a.
39
What is the result of (x^2)^3?
x^6
40
What does the expression (a*b)^n equal?
a^n * b^n
41
True or False: The cube root of a number is unique.
True
42
What is the value of 8^(1/3)?
2
43
Fill in the blank: The expression (x^2)(x^3)(x^4) simplifies to ____.
x^9
44
What is the value of √(x^4)?
x^2
45
What does it mean when we say a number is raised to the first power?
It means the number remains unchanged.
46
What is the result of 3^2 + 4^2?
25
47
What is the definition of a negative exponent?
A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent.
48
Fill in the blank: The expression 16^(1/4) is equal to ____.
2
49
What is the value of (x^5)(x^(-2))?
x^3
50
True or False: The product of two powers with the same base adds their exponents.
True
51
What is the value of 2^3 * 2^(-3)?
1
52
Fill in the blank: The expression a^m / a^n simplifies to ____.
a^(m-n)
53
What is the result of (5^2)^3?
5^6 or 15625
54
If a = 3, what is a^4?
81
55
What is the value of 1^n for any n?
1
56
What is the term for the number of times a base is multiplied by itself?
Exponent
57
Fill in the blank: The expression (x^0) equals ____.
1
58
What is the result of 2^(3+2)?
32

pre calc (2 decks)

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