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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. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Subtract the exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
cube-root key
the radical sign with a little 3 that indicates the cube root:

2. 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.
radical sign
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
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
move the decimal point the same number of units to the left

3. 1^4 =
Subtract the exponent
move the decimal point the same number of units to the left
1
rewrite one of the terms so that the exponents are equal

4. 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.
must be multiples of 3 or 0
exponent
When moving the decimal point to the left (dividing by 10)
perfect square

5. When moving the decimal point to the right (multiplying by 10)
To multiply powers that have the same base:
change both terms in order to keep the value the same.
decrease the value of the exponent by 1 (dividing by 10)
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

6. 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
To multiply powers that have the same base:
change both terms in order to keep the value the same.
10^-2
0

7. A negative exponent does not mean the decimal value is negative. It means the decimal value is
Same base
a fractional decimal
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
exponent

8. Valid powers-of-10 for engineering notation
3
To multiply powers that have the same base:
move the decimal point the same number of units to the right
must be multiples of 3 or 0

9. The decimal part
coefficient
square root
Not
Same base

10. To divide powers of 10:
exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Step 1. Divide the coefficients of the terms
cube root

11. Negative cube roots are okay ... negative square roots are
1
Not
2 x 10^9
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

12. 10 - or 1 with the decimal point moved one place to the right
0
same exponent
10^1
cubed

13. Any number with a negative exponent is equal to
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Are Equal
1 divided by that number with a positive exponent
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.

14. Increase the value of the exponent by 1 (multiplying by 10)
When moving the decimal point to the left (dividing by 10)
Not
10^-18
Are Equal

15. 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
Because 4 multiplied by itself equals 16.
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
Moving the decimal point to the right
cube-root key

16. 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
same exponent
10^2
radical sign
Because 4 multiplied by itself equals 16.

17. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
proper scientific
base
a fractional decimal
1

18. 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
negative number
decrease the power-of-10 exponent by the same number of units
adjust the value of the coefficient
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

19. Indicates the number of times the base is to be multiplied.
10^1
Are Equal
exponent
6.74 x 10^-7

20. To find the square root of any number - simply key in the number (the radicand) and press the
Calculator square-root key
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
perfect square
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

21. When you change the position of the decimal point in a coefficient value
When the exponent of a power-of-10 expression is a negative integer:
0
a fractional decimal
you have to adjust the value of the exponent in order avoid changing the actual value.

22. Dividing by 10
Moving the decimal point to the left
Step 1. Rewrite each number 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
you have to adjust the value of the exponent in order avoid changing the actual value.

23. When you increase the value of the power-of-10 exponent
base
move the decimal point the same number of units to the left
0
decrease the power-of-10 exponent by the same number of units

24. 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
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
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. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
cube root

25. When you move the decimal point in the coefficient to the left
increase the power-of-10 exponent by the same number of units
decrease the value of the exponent by 1 (dividing by 10)
1
10^2

26. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
same exponent
1
When the exponent of a power-of-10 expression is a negative integer:

27. The square of 3 is
9 (3^2 = 9)
one digit to the left of the decimal point
exponent
rewrite one of the terms so that the exponents are equal

28. Always 10 for scientific notation
The solution exists - but not in the real number system.
base
Are Equal
10^-18

29. To subtract powers of ten:
The solution exists - but not in the real number system.
Not
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
decrease the value of the exponent by 1 (dividing by 10)

30. 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.
squared
10^2
Scientific notation
exponent

31. To divide powers of ten:
Moving the decimal point to the left
1. Divide the coefficients 2. Subtract the exponents
the radical sign with a little 3 that indicates the cube root:
When the exponent of a power-of-10 expression is a negative integer:

32. 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.
When the exponent of a power-of-10 expression is a negative integer:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
6.74 x 10^-7
a fractional decimal

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

34. 1 to any power is equal to
Because 4 multiplied by itself equals 16.
1. Multiply the coefficients 2. Add the exponents
10^-1
1

35. A very small number such as 0.000000674 can be written with scientific notation as
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
6.74 x 10^-7
exponent
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.

36. When you move the decimal point in the coefficient to the right
1. Multiply the coefficients 2. Add the exponents
decrease the power-of-10 exponent by the same number of units
base
Because 4 multiplied by itself equals 16.

37. For the 10
squared
must be multiples of 3 or 0
exponent
coefficient

38. A number is a second number which - when multiplied by itself three times - equals the original number.
6.74 x 10^-7
negative number
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
cube root

39. Step 1: Add the exponents Step 2: Use the common base
When the exponent of a power-of-10 expression is a negative integer:
change both terms in order to keep the value the same.
10^-18
To multiply powers that have the same base:

40. The square root of zero is
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
To multiply powers that have the same base:
0
1 divided by that number with a positive exponent

41. A number - when multiplied by itself - is equal to a given number.
Are Equal
square root
1
cubed

42. A number with an exponent of 2 is often said to be
Engineering notation
1. Multiply the coefficients 2. Add the exponents
squared
Subtract the exponent

43. When the exponents are not the same
negative number
Moving the decimal point to the left
square root
rewrite one of the terms so that the exponents are equal

44. 5^1 =
Because 4 multiplied by itself equals 16.
10^-2
base
5

45. What number multiplied by itself is equal to 16? The answer is 4. Why?
Because 4 multiplied by itself equals 16.
Calculator square-root key
squared
cubed

46. 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.
0
Engineering notation
same exponent
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.

47. Numbers with exponents can be directly multiplied or divided only when they have the
10^-1
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
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

48. Indicates the number to be multiplied.
cubed
0
base
move the decimal point the same number of units to the right

49. The symbol for the cube root of a number is
the radical sign with a little 3 that indicates the cube root:
When moving the decimal point to the left (dividing by 10)
1. Multiply the coefficients 2. Add the exponents
exponent

50. 1 to any power is equal to
10^-1
the radical sign with a little 3 that indicates the cube root:
Calculator square-root key
1