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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. 1 to any power is equal to
move the decimal point the same number of units to the left
rewrite one of the terms so that the exponents are equal
same exponent
1

2. When moving the decimal point to the right (multiplying by 10)
decrease the value of the exponent by 1 (dividing by 10)
0
increase the power-of-10 exponent by the same number of units
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

3. When you change the position of the decimal point in a coefficient value
10^1
proper scientific
1
you have to adjust the value of the exponent in order avoid changing the actual value.

4. Negative cube roots are okay ... negative square roots are
Not
exponent
0
cube root

5. 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
exponent
radical sign
10^-2

6. Increase the value of the exponent by 1 (multiplying by 10)
base
5
1
When moving the decimal point to the left (dividing by 10)

7. When you move the decimal point in the coefficient to the right
decrease the power-of-10 exponent by the same number of units
adjust the value of the coefficient
cube-root key
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

8. To multiply powers of 10:
0
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.
Because 4 multiplied by itself equals 16.
change both terms in order to keep the value the same.

9. 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.
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
When the exponent of a power-of-10 expression is a negative integer:
5

10. 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
exponent
Step 1. Divide the coefficients of the terms
2

11. 1^4 =
1
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1. Multiply the coefficients 2. Add the exponents
Step 1. Divide the coefficients of the terms

12. The square root of zero is
0
10^-1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^-2

13. 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
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
6.74 x 10^-7
one digit to the left of the decimal point
change both terms in order to keep the value the same.

14. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
cube root
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
When the exponent of a power-of-10 expression is a negative integer:

15. The square of 3 is
9 (3^2 = 9)
Because 4 multiplied by itself equals 16.
adjust the value of the coefficient
1

16. To subtract powers of ten:
negative number
Calculator square-root key
decrease the power-of-10 exponent by the same number of units
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

17. 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
2
adjust the value of the coefficient
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1

18. When the exponents are not the same
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
must be multiples of 3 or 0
decrease the power-of-10 exponent by the same number of units
rewrite one of the terms so that the exponents are equal

19. To add powers of ten:
radical sign
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
Calculator square-root key

20. Represents 1 preceded by 17 zeros and a decimal point.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
coefficient
10^-18
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

21. A negative exponent does not mean the decimal value is negative. It means the decimal value is
When moving the decimal point to the left (dividing by 10)
Moving the decimal point to the right
Subtract the exponent
a fractional decimal

22. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
10^-2
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
adjust the value of the coefficient
proper scientific

23. 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
10^1
negative number

24. A very small number such as 0.000000674 can be written with scientific notation as
6.74 x 10^-7
10^-2
must be multiples of 3 or 0
1 divided by that number with a positive exponent

25.
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
rewrite one of the terms so that the exponents are equal
10^-2
cube root

26. A number - when multiplied by itself - is equal to a given number.
change both terms in order to keep the value the same.
square root
Not
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

27. Multiplying by 10
Moving the decimal point to the right
coefficient
0
1. Multiply the coefficients 2. Add the exponents

28. To divide powers of 10:
same exponent
When the exponent of a power-of-10 expression is a negative integer:
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
Step 1. Divide the coefficients of the terms

29. Step 1: Add the exponents Step 2: Use the common base
rewrite one of the terms so that the exponents are equal
10^1
Calculator square-root key
To multiply powers that have the same base:

30. When you increase the value of the power-of-10 exponent
1
When the exponent of a power-of-10 expression is a negative integer:
2
move the decimal point the same number of units to the left

31. When you decrease the value of the power-of-10 exponent
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
one digit to the left of the decimal point
move the decimal point the same number of units to the right
radical sign

32. 3^0 =
exponent
1
6.74 x 10^-7
change both terms in order to keep the value the same.

33. 0^5 =
When the exponent of a power-of-10 expression is a negative integer:
6.74 x 10^-7
change both terms in order to keep the value the same.
0

34. 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
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
6.74 x 10^-7
cube-root key
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

35. = 0.01 - or 1 with the decimal point moved two places to the left.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^-2
Because 4 multiplied by itself equals 16.
When the exponent of a power-of-10 expression is a negative integer:

36. Don't bother trying to find the square root of a negative number.
The solution exists - but not in the real number system.
Because 4 multiplied by itself equals 16.
0
1

37. To add or subtract numbers written with exponents:
1
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
negative number
Step 1. Divide the coefficients of the terms

38. To find the square root of any number - simply key in the number (the radicand) and press the
coefficient
0
Calculator square-root key
Moving the decimal point to the right

39. Indicates the number to be multiplied.
one digit to the left of the decimal point
Scientific notation
Moving the decimal point to the right
base

40. 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.
base
Subtract the exponent
Engineering notation
coefficient

41. Indicates the number of times the base is to be multiplied.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Because 4 multiplied by itself equals 16.
exponent
Engineering notation

42. When you move the decimal point in the coefficient to the left
1. Divide the coefficients 2. Subtract the exponents
cubed
increase the power-of-10 exponent by the same number of units
decrease the value of the exponent by 1 (dividing by 10)

43. The symbol for the cube root of a number is
1
must be multiples of 3 or 0
the radical sign with a little 3 that indicates the cube root:
rewrite one of the terms so that the exponents are equal

44. 100 - or 1 with the decimal point moved two places to the right
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
adjust the value of the coefficient
10^2
increase the power-of-10 exponent by the same number of units

45. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Same base
Subtract the exponent
squared
rewrite one of the terms so that the exponents are equal

46. A number with an exponent of 3 is often said to be
0
cube-root key
cubed
2 x 10^9

47. What number multiplied by itself is equal to 16? The answer is 4. Why?
Because 4 multiplied by itself equals 16.
10^2
itself
Same base

48. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
1. Multiply the coefficients 2. Add the exponents
Moving the decimal point to the left
Subtract the exponent

49. 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
exponent
rewrite one of the terms so that the exponents are equal
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
Are Equal

50. To multiply powers of ten:
Moving the decimal point to the right
10^1
Moving the decimal point to the left
1. Multiply the coefficients 2. Add the exponents