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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 very small number such as 0.000000674 can be written with scientific notation as
change both terms in order to keep the value the same.
decrease the value of the exponent by 1 (dividing by 10)
3
6.74 x 10^-7

2. A number with an exponent of 2 is often said to be
squared
proper scientific
The solution exists - but not in the real number system.
rewrite one of the terms so that the exponents are equal

3. 5^1 =
move the decimal point the same number of units to the left
radical sign
5
cube root

4. A number - when multiplied by itself - is equal to a given number.
cubed
rewrite one of the terms so that the exponents are equal
same exponent
square root

5. Represents 1 preceded by 17 zeros and a decimal point.
perfect square
10^-18
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Engineering notation

6. = 0.01 - or 1 with the decimal point moved two places to the left.
increase the power-of-10 exponent by the same number of units
a fractional decimal
0
10^-2

7. To multiply or divide exponent terms that do not have the same base:
move the decimal point the same number of units to the left
1
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Subtract the exponent

8. A negative exponent does not mean the decimal value is negative. It means the decimal value is
1
exponent
a fractional decimal
one digit to the left of the decimal point

9. Valid powers of 10 for engineering notation are:
cube root
same exponent
Engineering notation
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

10. = 0.1 - or 1 with the decimal point moved one place to the left.
10^-1
cube-root key
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1

11. For the 10
base
square root
10^-1
exponent

12. 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
must be multiples of 3 or 0
1. Multiply the coefficients 2. Add the exponents
10^-18
adjust the value of the coefficient

13. 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.
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)

14. 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.
Same base
Scientific notation
Engineering notation
increase the power-of-10 exponent by the same number of units

15. There are no special rules for adding and subtracting numbers that are written with exponents.
a fractional decimal
To multiply powers that have the same base:
Same base
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

16. A number with an exponent of 3 is often said to be
0
exponent
1. Divide the coefficients 2. Subtract the exponents
cubed

17. Valid powers-of-10 for engineering notation
Step 1. Divide the coefficients of the terms
base
must be multiples of 3 or 0
Because 4 multiplied by itself equals 16.

18. To subtract 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
Because 4 multiplied by itself equals 16.
1. Multiply the coefficients 2. Add the exponents
Same base

19. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
decrease the power-of-10 exponent by the same number of units
proper scientific
perfect square
The solution exists - but not in the real number system.

20. When you move the decimal point in the coefficient to the right
Scientific notation
1
decrease the power-of-10 exponent by the same number of units
1

21. Any number with a negative exponent is equal to
1 divided by that number with a positive exponent
move the decimal point the same number of units to the left
Step 1. Divide the coefficients of the terms
Moving the decimal point to the right

22. 100 - or 1 with the decimal point moved two places to the right
10^-2
increase the power-of-10 exponent by the same number of units
Not
10^2

23. 3^0 =
itself
you have to adjust the value of the exponent in order avoid changing the actual value.
1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

24. Increase the value of the exponent by 1 (multiplying by 10)
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Moving the decimal point to the left
cube root
When moving the decimal point to the left (dividing by 10)

25. To multiply powers of ten:
The solution exists - but not in the real number system.
move the decimal point the same number of units to the left
1. Multiply the coefficients 2. Add the exponents
0

26. 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.
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
cubed
perfect square
1. Multiply the coefficients 2. Add the exponents

27. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
1. Multiply the coefficients 2. Add the exponents
base
cubed

28. To divide powers of ten:
exponent
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1. Divide the coefficients 2. Subtract the exponents
1

29. What number multiplied by itself is equal to 16? The answer is 4. Why?
Same base
10^2
Because 4 multiplied by itself equals 16.
1. Divide the coefficients 2. Subtract the exponents

30. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
the radical sign with a little 3 that indicates the cube root:
2 x 10^9
perfect square
10^-18

31. 1^4 =
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.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1
When the exponent of a power-of-10 expression is a negative integer:

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.
0
1
adjust the value of the coefficient

33. Powers of ten can be added or subtracted only when their exponents
rewrite one of the terms so that the exponents are equal
Are Equal
2
Same base

34. Step 1: Add the exponents Step 2: Use the common base
To multiply powers that have the same base:
0
squared
1 divided by that number with a positive exponent

35. 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
Because 4 multiplied by itself equals 16.
move the decimal point the same number of units to the right
change both terms in order to keep the value the same.
radical sign

36. Numbers with exponents can be directly multiplied or divided only when they have the
same exponent
Because 4 multiplied by itself equals 16.
a fractional decimal
Same base

37. The square root of 9 is
The solution exists - but not in the real number system.
base
3
radical sign

38. The decimal part
squared
When moving the decimal point to the left (dividing by 10)
coefficient
10^2

39. 1 to any power is equal to
1
coefficient
exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

40. 0^5 =
0
3
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

41. To multiply powers of 10:
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.
Scientific notation
0
decrease the value of the exponent by 1 (dividing by 10)

42. Any number with an exponent of 0 is equal to
1
adjust the value of the coefficient
10^2
the radical sign with a little 3 that indicates the cube root:

43. Multiplying by 10
Moving the decimal point to the right
1
proper scientific
Engineering notation

44. The cube root of zero is
cube root
0
adjust the value of the coefficient
1

45. The square root of zero is
square root
exponent
decrease the value of the exponent by 1 (dividing by 10)
0

46. Don't bother trying to find the square root of a negative number.
The solution exists - but not in the real number system.
move the decimal point the same number of units to the left
0
radical sign

47. The square of 3 is
2
9 (3^2 = 9)
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
cube-root key

48. 1 to any power is equal to
the radical sign with a little 3 that indicates the cube root:
1
cube root
Step 1. Divide the coefficients of the terms

49. Negative cube roots are okay ... negative square roots are
Not
2 x 10^9
0
Moving the decimal point to the right

50. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
decrease the power-of-10 exponent by the same number of units
cubed
2
exponent