Test your basic knowledge |

CLEP General Mathematics: Powers Exponents And Roots

Subjects : clep, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. To multiply powers of ten:
cube-root key
1
base
1. Multiply the coefficients 2. Add the exponents

2. To add or subtract numbers written with exponents:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
rewrite one of the terms so that the exponents are equal
2 x 10^9
1

3. 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
5
10^-2
move the decimal point the same number of units to the left
change both terms in order to keep the value the same.

4. Any number with an exponent of 1 is equal to
itself
Moving the decimal point to the right
proper scientific
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

5. = 0.01 - or 1 with the decimal point moved two places to the left.
Same base
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
When moving the decimal point to the left (dividing by 10)
10^-2

6. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
Are Equal
Because 4 multiplied by itself equals 16.
exponent
proper scientific

7. Indicates the number of times the base is to be multiplied.
cube-root key
When moving the decimal point to the left (dividing by 10)
exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

8. Step 1: Add the exponents Step 2: Use the common base
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
the radical sign with a little 3 that indicates the cube root:
adjust the value of the coefficient

9. The cube root of zero is
you have to adjust the value of the exponent in order avoid changing the actual value.
1. Divide the coefficients 2. Subtract the exponents
squared
0

10. Powers of ten can be added or subtracted only when their exponents
When the exponent of a power-of-10 expression is a negative integer:
must be multiples of 3 or 0
Subtract the exponent
Are Equal

11. To divide powers of ten:
The solution exists - but not in the real number system.
1. Divide the coefficients 2. Subtract the exponents
cube-root key
Subtract the exponent

12. A number with an exponent of 2 is often said to be
adjust the value of the coefficient
exponent
squared
move the decimal point the same number of units to the left

13. The square of 3 is
10^1
Calculator square-root key
9 (3^2 = 9)
Not

14. When you move the decimal point in the coefficient to the right
10^2
adjust the value of the coefficient
a fractional decimal
decrease the power-of-10 exponent by the same number of units

15. 1^4 =
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
1
Scientific notation
move the decimal point the same number of units to the right

16. The square root of 9 is
3
squared
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
The solution exists - but not in the real number system.

17. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
rewrite one of the terms so that the exponents are equal
2
itself
move the decimal point the same number of units to the right

18. When you move the decimal point in the coefficient to the left
Moving the decimal point to the left
move the decimal point the same number of units to the right
increase the power-of-10 exponent by the same number of units
itself

19. A number is a second number which - when multiplied by itself three times - equals the original number.
proper scientific
Calculator square-root key
cube-root key
cube root

20. A very small number such as 0.000000674 can be written with scientific notation as
6.74 x 10^-7
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
negative number
Moving the decimal point to the left

21. 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.
Moving the decimal point to the right
1
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
radical sign

22. 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
Moving the decimal point to the right
one digit to the left of the decimal point
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

23. Scientific notation requires there to be only
increase the power-of-10 exponent by the same number of units
square root
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
one digit to the left of the decimal point

24. To divide powers that have the same base:
0
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
0
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

25. 5^1 =
When moving the decimal point to the left (dividing by 10)
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
5
decrease the power-of-10 exponent by the same number of units

26. To divide powers of 10:
must be multiples of 3 or 0
Scientific notation
10^1
Step 1. Divide the coefficients of the terms

27. The decimal part
Are Equal
0
coefficient
the radical sign with a little 3 that indicates the cube root:

28. When moving the decimal point to the right (multiplying by 10)
must be multiples of 3 or 0
cubed
Are Equal
decrease the value of the exponent by 1 (dividing by 10)

29. 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
increase the power-of-10 exponent by the same number of units
1
cube-root key
Are Equal

30. 1 to any power is equal to
1
2
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
adjust the value of the coefficient

31. Numbers with exponents can be directly multiplied or divided only when they have the
0
Same base
one digit to the left of the decimal point
2

32. The square root of zero is
0
squared
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
increase the power-of-10 exponent by the same number of units

33. Negative cube roots are okay ... negative square roots are
the radical sign with a little 3 that indicates the cube root:
Not
coefficient
square root

34. When you increase the value of the power-of-10 exponent
0
2 x 10^9
move the decimal point the same number of units to the left
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

35. To add powers of ten:
perfect square
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
0
itself

36. To multiply powers of 10:
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
increase the power-of-10 exponent by the same number of units
base
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.

37. A number with an exponent of 3 is often said to be
change both terms in order to keep the value the same.
one digit to the left of the decimal point
cubed
decrease the power-of-10 exponent by the same number of units

38. 0^5 =
0
base
Subtract the exponent
1. Divide the coefficients 2. Subtract the exponents

39. 0 to any power is equal to
the radical sign with a little 3 that indicates the cube root:
10^-18
Subtract the exponent
0

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

41. For the 10
move the decimal point the same number of units to the left
exponent
1
10^-1

42. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
must be multiples of 3 or 0
10^2
2 x 10^9
1. Multiply the coefficients 2. Add the exponents

43. When the exponents are not the same
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
same exponent
exponent
rewrite one of the terms so that the exponents are equal

44. 10 - or 1 with the decimal point moved one place to the right
10^1
cube-root key
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
perfect square

45. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
10^2
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
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.

46. 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
10^-1
adjust the value of the coefficient
When moving the decimal point to the left (dividing by 10)
Not

47. A number - when multiplied by itself - is equal to a given number.
3
square root
Because 4 multiplied by itself equals 16.
Not

48. Valid powers-of-10 for engineering notation
change both terms in order to keep the value the same.
0
must be multiples of 3 or 0
1

49. What number multiplied by itself is equal to 16? The answer is 4. Why?
Because 4 multiplied by itself equals 16.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
the radical sign with a little 3 that indicates the cube root:
Subtract the exponent

50. Valid powers of 10 for engineering notation are:
Not
When the exponent of a power-of-10 expression is a negative integer:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
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