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CLEP General Mathematics: Powers Exponents And Roots

Subjects : clep, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
Scientific notation
Engineering notation
adjust the value of the coefficient

2. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
move the decimal point the same number of units to the left
move the decimal point the same number of units to the right
Because 4 multiplied by itself equals 16.

3. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
increase the power-of-10 exponent by the same number of units
Subtract the exponent
Because the exponent for the base-10 must be 0 or a multiple of 3 - the coefficient cannot always be a value between -9 and 9. Instead - the coefficients for engineering notation will be between
The solution exists - but not in the real number system.

4. An integer that is found by squaring another integer. You already know how to find the square root of 25 because it is a perfect square: 5 x 5 = 25 - or you could write it as 52 = 25. So 25 is a perfect square - and its square root is 5.
1
exponent
10^-2
perfect square

5. When you move the decimal point in the coefficient to the right
10^2
decrease the power-of-10 exponent by the same number of units
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
proper scientific

6. The square root of zero is
To multiply powers that have the same base:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
0
Subtract the exponent

7. Represents 1 preceded by 17 zeros and a decimal point.
0
perfect square
must be multiples of 3 or 0
10^-18

8. The cube root of a negative number is also a
negative number
Engineering notation
decrease the power-of-10 exponent by the same number of units
a fractional decimal

9. A very small number such as 0.000000674 can be written with scientific notation as
1. Multiply the coefficients 2. Add the exponents
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
6.74 x 10^-7
0

10. The square of 3 is
When the exponent of a power-of-10 expression is a negative integer:
1
1
9 (3^2 = 9)

11. For the 10
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
6.74 x 10^-7
10^2
exponent

12. Numbers with exponents can be directly multiplied or divided only when they have the
decrease the power-of-10 exponent by the same number of units
a fractional decimal
1
Same base

13. To divide powers that have the same base:
1
cube-root key
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

14. To add or subtract numbers written with exponents:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
10^1
a fractional decimal
proper scientific

15. 0 to any power is equal to
10^-2
0
negative number
1 divided by that number with a positive exponent

16. Indicates the number to be multiplied.
base
When the exponent of a power-of-10 expression is a negative integer:
0
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

17. When you increase the value of the power-of-10 exponent
Same base
Are Equal
Not
move the decimal point the same number of units to the left

18. A negative exponent does not mean the decimal value is negative. It means the decimal value is
10^-1
cube root
a fractional decimal
0

19. There are no special rules for adding and subtracting numbers that are written with exponents.
cubed
10^-2
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
base

20. 10^-1 = 0.1 - or 1 with the decimal point moved one place to the left. 10^-2 = 0.01 - or 1 with the decimal point moved two places to the left. 10^-18 represents 1 preceded by 17 zeros and a decimal point.
When moving the decimal point to the left (dividing by 10)
When the exponent of a power-of-10 expression is a negative integer:
Engineering notation
cube root

21. The decimal part
radical sign
coefficient
10^-18
same exponent

22. Allows you to express very large and very small numbers without using large numbers of digits and decimal places. It's all done with powers of ten.
base
Scientific notation
Calculator square-root key
radical sign

23. 1^4 =
Determine the number of times the original decimal has to be multiplied or divided by 10 in order to show one non-zero digit to the left of the decimal point. Multiply the normalized value by a power of 10 that will restore equality. If you multiplie
1
Step 1. Multiply the coefficients of the factors. The result is the coefficient of the product. Step 2. Add the exponents of the factors. The result is the exponent of the product. Of course the base of 10 remains unchanged.
perfect square

24. Multiplying by 10
move the decimal point the same number of units to the left
10^1
Moving the decimal point to the right
one digit to the left of the decimal point

25. The symbol for the cube root of a number is
10^-18
the radical sign with a little 3 that indicates the cube root:
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
negative number

26. When the exponents are not the same
1
rewrite one of the terms so that the exponents are equal
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^2

27. To divide powers of ten:
Moving the decimal point to the left
1
base
1. Divide the coefficients 2. Subtract the exponents

28. Powers of ten can be added or subtracted only when their exponents
a fractional decimal
0
Same base
Are Equal

29. 10 - or 1 with the decimal point moved one place to the right
Moving the decimal point to the left
5
10^1
To multiply powers that have the same base:

30. Is a special form of power-of-10 notation where the exponents for the 10s must be 0 or multiples of 3. There must be 1 - 2 - or 3 digits on the left side of the decimal point.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Engineering notation
3
radical sign

31. A number with an exponent of 3 is often said to be
Not
10^-1
cubed
0

32. To find the cube root of any number - simply key in the number (the radicand) and press cube-root key. On most calculators - the cube-root function is a 2nd level function. This means you have to press the 2nd key before pressing the key for the
decrease the value of the exponent by 1 (dividing by 10)
rewrite one of the terms so that the exponents are equal
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
cube-root key

33. The symbol for the square root of a number is the - a sign placed in front of an expression to denote that a root is to be extracted.
radical sign
same exponent
1
3

34.
5
3
Determine the number of times the original decimal has to be multiplied or divided by 10 in order to show one non-zero digit to the left of the decimal point. Multiply the normalized value by a power of 10 that will restore equality. If you multiplie
increase the power-of-10 exponent by the same number of units

35. 1 to any power is equal to
cubed
1
move the decimal point the same number of units to the right
Not

36. Dividing by 10
1
square root
Moving the decimal point to the left
When moving the decimal point to the left (dividing by 10)

37. To divide powers of 10:
The solution exists - but not in the real number system.
Step 1. Divide the coefficients of the terms
Not
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

38. What number multiplied by itself is equal to 16? The answer is 4. Why?
cubed
The solution exists - but not in the real number system.
Because 4 multiplied by itself equals 16.
10^2

39. Valid powers-of-10 for engineering notation
10^1
1
1. Multiply the coefficients 2. Add the exponents
must be multiples of 3 or 0

40. When working with powers of ten and scientific notation it is often necessary to adjust the position of the decimal point in the coefficient or to change the value of the exponent. When changing one of these terms - it is important that
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
exponent
9 (3^2 = 9)
change both terms in order to keep the value the same.

41. Because the exponent for the base-10 must be 0 or a multiple of 3 - the coefficient cannot always be a value between -9 and 9. Instead - the coefficients for engineering notation will be between
square root
The solution exists - but not in the real number system.
Because the exponent for the base-10 must be 0 or a multiple of 3 - the coefficient cannot always be a value between -9 and 9. Instead - the coefficients for engineering notation will be between
9 (3^2 = 9)

42. 0^5 =
Not
10^-18
base
0

43. The square root of 9 is
9 (3^2 = 9)
1 divided by that number with a positive exponent
3
The solution exists - but not in the real number system.

44. Step 1: Add the exponents Step 2: Use the common base
2
10^-1
9 (3^2 = 9)
To multiply powers that have the same base:

45. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
Scientific notation
5
2
square root

46. To multiply powers of ten:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
perfect square
1. Multiply the coefficients 2. Add the exponents
decrease the value of the exponent by 1 (dividing by 10)

47. To multiply powers of 10:
decrease the power-of-10 exponent by the same number of units
radical sign
Step 1. Multiply the coefficients of the factors. The result is the coefficient of the product. Step 2. Add the exponents of the factors. The result is the exponent of the product. Of course the base of 10 remains unchanged.
9 (3^2 = 9)

48. Negative cube roots are okay ... negative square roots are
5
Scientific notation
Not
1

49. Always 10 for scientific notation
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
base
increase the power-of-10 exponent by the same number of units
decrease the power-of-10 exponent by the same number of units

50. A number - when multiplied by itself - is equal to a given number.
square root
0
Step 1. Multiply the coefficients of the factors. The result is the coefficient of the product. Step 2. Add the exponents of the factors. The result is the exponent of the product. Of course the base of 10 remains unchanged.
adjust the value of the coefficient