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

2. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
a fractional decimal
Subtract the exponent
0
base

3. When you increase the value of the power-of-10 exponent
9 (3^2 = 9)
move the decimal point the same number of units to the left
To multiply powers that have the same base:
base

4. 1 to any power is equal to
1
radical sign
Not
exponent

5. Indicates the number to be multiplied.
1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
base
decrease the power-of-10 exponent by the same number of units

6. Any number with an exponent of 1 is equal to
base
Because 4 multiplied by itself equals 16.
itself
0

7. The square root of 9 is
Because 4 multiplied by itself equals 16.
3
exponent
0

8. To multiply or divide exponent terms that do not have the same base:
coefficient
same exponent
1 divided by that number with a positive exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

9. 1 to any power is equal to
1 divided by that number with a positive exponent
negative number
1
To multiply powers that have the same base:

10. To add or subtract numbers written with exponents:
negative number
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
0
square root

11. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
Step 1. Divide the coefficients of the terms
cubed
2 x 10^9
1

12. Step 1: Add the exponents Step 2: Use the common base
The solution exists - but not in the real number system.
0
0
To multiply powers that have the same base:

13. 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.
squared
exponent
base
Engineering notation

14. Powers of ten can be added or subtracted only when their exponents
Moving the decimal point to the right
Are Equal
10^1
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.

15. 3^0 =
base
Subtract the exponent
1
10^-18

16. Scientific notation requires there to be only
Subtract the exponent
6.74 x 10^-7
exponent
one digit to the left of the decimal point

17. 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
1
proper scientific
9 (3^2 = 9)

18. 100 - or 1 with the decimal point moved two places to the right
6.74 x 10^-7
1
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^2

19. When you change the position of the decimal point in a coefficient value
Are Equal
negative number
you have to adjust the value of the exponent in order avoid changing the actual value.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

20. Valid powers-of-10 for engineering notation
must be multiples of 3 or 0
increase the power-of-10 exponent by the same number of units
10^-1
Moving the decimal point to the right

21. Any number with an exponent of 0 is equal to
you have to adjust the value of the exponent in order avoid changing the actual value.
1
move the decimal point the same number of units to the right
Step 1. Divide the coefficients of the terms

22. 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
1. Divide the coefficients 2. Subtract the exponents
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
1

23. There are no special rules for adding and subtracting numbers that are written with exponents.
Subtract the exponent
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
rewrite one of the terms so that the exponents are equal
proper scientific

24. To subtract powers of ten:
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Not
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. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

25. 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
proper scientific
Calculator square-root key
Moving the decimal point to the right
same exponent

26. Always 10 for scientific notation
2 x 10^9
2
base
9 (3^2 = 9)

27.
cube-root key
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
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
cubed

28. A number is a second number which - when multiplied by itself three times - equals the original number.
0
The solution exists - but not in the real number system.
Step 1. Divide the coefficients of the terms
cube root

29. 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
adjust the value of the coefficient
0
exponent
1. Divide the coefficients 2. Subtract the exponents

30. The symbol for the cube root of a number is
must be multiples of 3 or 0
3
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
the radical sign with a little 3 that indicates the cube root:

31. A number with an exponent of 3 is often said to be
exponent
cube root
1
cubed

32. 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
must be multiples of 3 or 0
The solution exists - but not in the real number system.
10^-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

33. 5^1 =
5
Not
move the decimal point the same number of units to the left
increase the power-of-10 exponent by the same number of units

34. Numbers with exponents can be directly multiplied or divided only when they have the
3
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Same base
The solution exists - but not in the real number system.

35. To multiply powers of 10:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
change both terms in order to keep the value the same.
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.
1

36. 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.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
squared
the radical sign with a little 3 that indicates the cube root:
radical sign

37. The cube root of a negative number is also a
1
exponent
negative number
decrease the power-of-10 exponent by the same number of units

38. To find the square root of any number - simply key in the number (the radicand) and press the
1
Calculator square-root key
10^1
increase the power-of-10 exponent by the same number of units

39. The square of 3 is
Moving the decimal point to the left
Not
9 (3^2 = 9)
10^-1

40. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
10^1
must be multiples of 3 or 0
decrease the power-of-10 exponent by the same number of units

41. Multiplying by 10
base
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Moving the decimal point to the right
1

42. A number - when multiplied by itself - is equal to a given number.
1
To multiply powers that have the same base:
you have to adjust the value of the exponent in order avoid changing the actual value.
square root

43. 0 to any power is equal to
1
0
cube root
1

44. 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.
Calculator square-root key
When the exponent of a power-of-10 expression is a negative integer:
1
rewrite one of the terms so that the exponents are equal

45. 10 - or 1 with the decimal point moved one place to the right
negative number
10^1
10^-18
0

46. 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.
0
Scientific notation
decrease the value of the exponent by 1 (dividing by 10)
cube root

47. For the 10
exponent
When moving the decimal point to the left (dividing by 10)
cube-root key
the radical sign with a little 3 that indicates the cube root:

48. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
1 divided by that number with a positive exponent
1. Divide the coefficients 2. Subtract the exponents
Calculator square-root key
2

49. When the exponents are not the same
cubed
rewrite one of the terms so that the exponents are equal
Moving the decimal point to the left
3

50. Don't bother trying to find the square root of a negative number.
The solution exists - but not in the real number system.
9 (3^2 = 9)
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base