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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. Indicates the number of times the base is to be multiplied.
exponent
Subtract the exponent
10^-1
Engineering notation

2. To divide powers of 10:
Step 1. Divide the coefficients of the terms
cubed
increase the power-of-10 exponent by the same number of units
change both terms in order to keep the value the same.

3. Valid powers-of-10 for engineering notation
coefficient
10^2
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
must be multiples of 3 or 0

4. When working with scientific notation - you are often required to change the location of the decimal point in the coefficient - but when you move the decimal point - you must
1. Divide the coefficients 2. Subtract the exponents
adjust the value of the coefficient
When the exponent of a power-of-10 expression is a negative integer:
exponent

5. To divide powers that have the same base:
0
10^2
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
must be multiples of 3 or 0

6. Any number with an exponent of 1 is equal to
1
Calculator square-root key
itself
same exponent

7. 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. Divide the coefficients 2. Subtract the exponents
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
cube-root key
perfect square

8. 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.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
radical sign
rewrite one of the terms so that the exponents are equal
The solution exists - but not in the real number system.

9. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
1
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
3

10. A number - when multiplied by itself - is equal to a given number.
10^-18
rewrite one of the terms so that the exponents are equal
Calculator square-root key
square root

11. When the exponents are not the same
1
rewrite one of the terms so that the exponents are equal
9 (3^2 = 9)
Step 1. Divide the coefficients of the terms

12. When you change the position of the decimal point in a coefficient value
the radical sign with a little 3 that indicates the cube root:
you have to adjust the value of the exponent in order avoid changing the actual value.
Not
cube root

13. A number is a second number which - when multiplied by itself three times - equals the original number.
Scientific notation
Because 4 multiplied by itself equals 16.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
cube root

14. Negative cube roots are okay ... negative square roots are
Not
To multiply powers that have the same base:
negative number
0

15. 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. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
change both terms in order to keep the value the same.
1. Divide the coefficients 2. Subtract the exponents
perfect square

16. 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
cube-root key
The solution exists - but not in the real number system.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
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

17. The square root of zero is
0
base
perfect square
1

18. When you increase the value of the power-of-10 exponent
move the decimal point the same number of units to the left
10^-2
Engineering notation
cube-root key

19. To add powers of ten:
cube-root key
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
must be multiples of 3 or 0
move the decimal point the same number of units to the left

20. For the 10
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the right
exponent
rewrite one of the terms so that the exponents are equal

21. The square root of 9 is
3
must be multiples of 3 or 0
When the exponent of a power-of-10 expression is a negative integer:
cube root

22. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
1
base
2
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

23. To multiply powers of ten:
10^-1
0
proper scientific
1. Multiply the coefficients 2. Add the exponents

24. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
0
move the decimal point the same number of units to the left
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
proper scientific

25. 1 to any power is equal to
adjust the value of the coefficient
a fractional decimal
1
6.74 x 10^-7

26. 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.
1. Divide the coefficients 2. Subtract the exponents
When the exponent of a power-of-10 expression is a negative integer:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
exponent

27. Any number with an exponent of 0 is equal to
itself
1
9 (3^2 = 9)
change both terms in order to keep the value the same.

28. To divide powers of ten:
increase the power-of-10 exponent by the same number of units
Because 4 multiplied by itself equals 16.
1. Divide the coefficients 2. Subtract the exponents
squared

29. The decimal part
negative number
coefficient
rewrite one of the terms so that the exponents are equal
10^-2

30. The square of 3 is
base
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
9 (3^2 = 9)
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

31. Don't bother trying to find the square root of a negative number.
radical sign
base
0
The solution exists - but not in the real number system.

32. To subtract powers of ten:
cube root
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
cubed

33. A very small number such as 0.000000674 can be written with scientific notation as
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
6.74 x 10^-7
10^1
move the decimal point the same number of units to the left

34. The cube root of a negative number is also a
itself
Same base
negative number
move the decimal point the same number of units to the left

35. Indicates the number to be multiplied.
adjust the value of the coefficient
base
10^2
2 x 10^9

36. There are no special rules for adding and subtracting numbers that are written with exponents.
The solution exists - but not in the real number system.
exponent
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1. Multiply the coefficients 2. Add the exponents

37. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
1
10^-18
1
Subtract the exponent

38. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
increase the power-of-10 exponent by the same number of units
coefficient
1

39. 0 to any power is equal to
decrease the value of the exponent by 1 (dividing by 10)
0
radical sign
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

40. 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.
1
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
Scientific notation
squared

41. 1^4 =
1
Subtract the exponent
The solution exists - but not in the real number system.
base

42. The cube root of zero is
6.74 x 10^-7
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.
0
coefficient

43. 10 - or 1 with the decimal point moved one place to the right
0
0
10^1
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

44. What number multiplied by itself is equal to 16? The answer is 4. Why?
Calculator square-root key
Because 4 multiplied by itself equals 16.
one digit to the left of the decimal point
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

45. Powers of ten can be added or subtracted only when their exponents
exponent
Are Equal
decrease the power-of-10 exponent by the same number of units
one digit to the left of the decimal point

46. 100 - or 1 with the decimal point moved two places to the right
a fractional decimal
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
10^2
3

47. 5^1 =
10^-1
5
10^2
0

48. Scientific notation requires there to be only
one digit to the left of the decimal point
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Same base
0

49. Always 10 for scientific notation
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
1
radical sign
base

50. 0^5 =
0
1
Step 1. Divide the coefficients of the terms
Calculator square-root key