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. 3^0 =
a fractional decimal
To multiply powers that have the same base:
Moving the decimal point to the right
1

2. When you move the decimal point in the coefficient to the right
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
cubed
decrease the power-of-10 exponent by the same number of units

3. 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
cube-root key
5
rewrite one of the terms so that the exponents are equal
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

4. Valid powers of 10 for engineering notation are:
itself
1
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
10^-1

5. Adding and subtracting powers of ten can be a bit more complicated than multiplying and dividing. The main problem is that powers of ten can be added or subtracted only when both terms have the
To multiply powers that have the same base:
negative number
same exponent
0

6. 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
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)
10^-18

7. Any number with a negative exponent is equal to
1 divided by that number with a positive exponent
change both terms in order to keep the value the same.
one digit to the left of the decimal point
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.

8. Powers of ten can be added or subtracted only when their exponents
adjust the value of the coefficient
Are Equal
Moving the decimal point to the right
decrease the value of the exponent by 1 (dividing by 10)

9. The decimal part
Are Equal
Step 1. Divide the coefficients of the terms
coefficient
1 divided by that number with a positive exponent

10. A number with an exponent of 3 is often said to be
rewrite one of the terms so that the exponents are equal
cubed
cube-root key
move the decimal point the same number of units to the right

11. = 0.1 - or 1 with the decimal point moved one place to the left.
0
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^-1
Calculator square-root key

12. When you change the position of the decimal point in a coefficient value
0
you have to adjust the value of the exponent in order avoid changing the actual value.
must be multiples of 3 or 0
proper scientific

13. When you increase the value of the power-of-10 exponent
increase the power-of-10 exponent by the same number of units
10^1
cubed
move the decimal point the same number of units to the left

14. Any number with an exponent of 1 is equal to
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
0
itself

15. When you decrease the value of the power-of-10 exponent
radical sign
base
move the decimal point the same number of units to the right
1

16. The square root of zero is
negative number
Subtract the exponent
0
coefficient

17. There are no special rules for adding and subtracting numbers that are written with exponents.
Scientific notation
Are Equal
base
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

18. To multiply or divide exponent terms that do not have the same base:
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1
Moving the decimal point to the left
2

19. 100 - or 1 with the decimal point moved two places to the right
1. Divide the coefficients 2. Subtract the exponents
10^2
5
adjust the value of the coefficient

20. To add powers of ten:
10^-18
1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
9 (3^2 = 9)

21. A number is a second number which - when multiplied by itself three times - equals the original number.
Moving the decimal point to the right
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
cube root
Subtract the exponent

22. When the exponents are not the same
When the exponent of a power-of-10 expression is a negative integer:
rewrite one of the terms so that the exponents are equal
same exponent
base

23. The symbol for the cube root of a number is
1
Because 4 multiplied by itself equals 16.
10^-1
the radical sign with a little 3 that indicates the cube root:

24. 0 to any power is equal to
base
5
When the exponent of a power-of-10 expression is a negative integer:
0

25. Indicates the number to be multiplied.
Calculator square-root key
10^1
base
cube-root key

26. A negative exponent does not mean the decimal value is negative. It means the decimal value is
0
adjust the value of the coefficient
a fractional decimal
proper scientific

27. What number multiplied by itself is equal to 16? The answer is 4. Why?
3
Moving the decimal point to the right
Scientific notation
Because 4 multiplied by itself equals 16.

28. 1^4 =
move the decimal point the same number of units to the left
1
Moving the decimal point to the right
2 x 10^9

29. The cube root of a negative number is also a
base
The solution exists - but not in the real number system.
negative number
1. Multiply the coefficients 2. Add the exponents

30. 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
Because 4 multiplied by itself equals 16.
10^-1
6.74 x 10^-7
adjust the value of the coefficient

31. Multiplying by 10
Moving the decimal point to the right
exponent
Because 4 multiplied by itself equals 16.
Are Equal

32. 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^-18
Scientific notation
1

33. To divide powers of 10:
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
Step 1. Divide the coefficients of the terms
1 divided by that number with a positive exponent

34. = 0.01 - or 1 with the decimal point moved two places to the left.
cubed
a fractional decimal
itself
10^-2

35. 10 - or 1 with the decimal point moved one place to the right
move the decimal point the same number of units to the right
10^1
5
same exponent

36. Always 10 for scientific notation
base
1
10^-18
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

37. Valid powers-of-10 for engineering notation
1
1
must be multiples of 3 or 0
rewrite one of the terms so that the exponents are equal

38. Any number with an exponent of 0 is equal to
Moving the decimal point to the right
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:
1

39. Scientific notation requires there to be only
one digit to the left of the decimal point
Because 4 multiplied by itself equals 16.
Not
proper scientific

40. Increase the value of the exponent by 1 (multiplying by 10)
When moving the decimal point to the left (dividing by 10)
itself
cubed
Because 4 multiplied by itself equals 16.

41. The square of 3 is
9 (3^2 = 9)
1
1
10^-2

42. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
10^-1
0
proper scientific
Subtract the exponent

43. 1 to any power is equal to
1
Step 1. Divide the coefficients of the terms
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
you have to adjust the value of the exponent in order avoid changing the actual value.

44. 5^1 =
5
Step 1. Divide the coefficients of the terms
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
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

45. 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.
perfect square
Engineering notation
9 (3^2 = 9)
1. Multiply the coefficients 2. Add the exponents

46. Represents 1 preceded by 17 zeros and a decimal point.
Calculator square-root key
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
exponent
10^-18

47. When moving the decimal point to the right (multiplying by 10)
0
decrease the value of the exponent by 1 (dividing by 10)
10^-2
The solution exists - but not in the real number system.

48. To multiply powers of ten:
move the decimal point the same number of units to the right
1. Multiply the coefficients 2. Add the exponents
proper scientific
Step 1. Divide the coefficients of the terms

49. To divide powers that have the same base:
adjust the value of the coefficient
proper scientific
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
0

50. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
6.74 x 10^-7
rewrite one of the terms so that the exponents are equal
increase the power-of-10 exponent by the same number of units
Subtract the exponent