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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. Any number with an exponent of 1 is equal to
you have to adjust the value of the exponent in order avoid changing the actual value.
itself
2 x 10^9
0

2. 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
cubed
When the exponent of a power-of-10 expression is a negative integer:
adjust the value of the coefficient
exponent

3. 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.
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.
perfect square
radical sign
same exponent

4. There are no special rules for adding and subtracting numbers that are written with exponents.
move the decimal point the same number of units to the left
adjust the value of the coefficient
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Calculator square-root key

5. = 0.1 - or 1 with the decimal point moved one place to the left.
The solution exists - but not in the real number system.
0
10^-1
cubed

6. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
must be multiples of 3 or 0
1 divided by that number with a positive exponent
proper scientific

7. To add or subtract numbers written with exponents:
base
When the exponent of a power-of-10 expression is a negative integer:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1

8. Don't bother trying to find the square root of a negative number.
adjust the value of the coefficient
The solution exists - but not in the real number system.
0
Subtract the exponent

9. For the 10
exponent
Are Equal
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
10^-2

10. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
0
Subtract the exponent
1
change both terms in order to keep the value the same.

11. Valid powers of 10 for engineering notation are:
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
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.

12. The symbol for the cube root of a number is
rewrite one of the terms so that the exponents are equal
Are Equal
1
the radical sign with a little 3 that indicates the cube root:

13. Step 1: Add the exponents Step 2: Use the common base
To multiply powers that have the same base:
0
9 (3^2 = 9)
1. Divide the coefficients 2. Subtract the exponents

14. Valid powers-of-10 for engineering notation
2 x 10^9
must be multiples of 3 or 0
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1

15. 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.
2 x 10^9
When the exponent of a power-of-10 expression is a negative integer:
6.74 x 10^-7
cubed

16. Any number with an exponent of 0 is equal to
When the exponent of a power-of-10 expression is a negative integer:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1
must be multiples of 3 or 0

17. A number with an exponent of 3 is often said to be
same exponent
9 (3^2 = 9)
cubed
radical sign

18. When you move the decimal point in the coefficient to the right
10^-2
itself
proper scientific
decrease the power-of-10 exponent by the same number of units

19. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
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.
change both terms in order to keep the value the same.
decrease the value of the exponent by 1 (dividing by 10)

20. When moving the decimal point to the right (multiplying by 10)
10^-1
Calculator square-root key
10^-2
decrease the value of the exponent by 1 (dividing by 10)

21. 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.
Engineering notation
move the decimal point the same number of units to the left
square root
Are Equal

22. 1 to any power is equal to
radical sign
move the decimal point the same number of units to the right
0
1

23. 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.
2
negative number
Scientific notation
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

24. Indicates the number of times the base is to be multiplied.
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
exponent
you have to adjust the value of the exponent in order avoid changing the actual value.

25. 3^0 =
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
1
Step 1. Divide the coefficients of the terms
3

26. 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.
1
adjust the value of the coefficient
9 (3^2 = 9)

27. A number - when multiplied by itself - is equal to a given number.
5
cube root
square root
10^-1

28. Dividing by 10
Moving the decimal point to the left
exponent
0
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

29. Indicates the number to be multiplied.
decrease the power-of-10 exponent by the same number of units
2 x 10^9
base
5

30. The cube root of a negative number is also a
negative number
base
2
Moving the decimal point to the right

31. 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
adjust the value of the coefficient
cube-root key
1. Multiply the coefficients 2. Add the exponents
coefficient

32. The decimal part
exponent
Step 1. Divide the coefficients of the terms
10^-2
coefficient

33. A negative exponent does not mean the decimal value is negative. It means the decimal value is
base
rewrite one of the terms so that the exponents are equal
10^1
a fractional decimal

34. A number with an exponent of 2 is often said to be
cube-root key
Same base
10^-2
squared

35. What number multiplied by itself is equal to 16? The answer is 4. Why?
proper scientific
Because 4 multiplied by itself equals 16.
Engineering notation
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

36. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Same base

37. A very small number such as 0.000000674 can be written with scientific notation as
6.74 x 10^-7
Subtract the exponent
Same base
2

38. Numbers with exponents can be directly multiplied or divided only when they have the
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
must be multiples of 3 or 0
Same base

39. To subtract powers of ten:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
3
Subtract the exponent

40. Negative cube roots are okay ... negative square roots are
Moving the decimal point to the left
Not
1
10^1

41. When you move the decimal point in the coefficient to the left
you have to adjust the value of the exponent in order avoid changing the actual value.
must be multiples of 3 or 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

42. 1^4 =
you have to adjust the value of the exponent in order avoid changing the actual value.
1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Subtract the exponent

43. Scientific notation requires there to be only
Moving the decimal point to the right
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
adjust the value of the coefficient
one digit to the left of the decimal point

44. 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.
decrease the power-of-10 exponent by the same number of units
0
radical sign
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

45. To multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
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.
Scientific notation

46. To add powers of ten:
squared
Because 4 multiplied by itself equals 16.
cubed
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

47. When you decrease the value of the power-of-10 exponent
change both terms in order to keep the value the same.
increase the power-of-10 exponent by the same number of units
move the decimal point the same number of units to the right
square root

48.
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
2
the radical sign with a little 3 that indicates the cube root:

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
cubed
decrease the power-of-10 exponent by the same number of units
Same base
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

50. The square root of zero is
you have to adjust the value of the exponent in order avoid changing the actual value.
1
1. Multiply the coefficients 2. Add the exponents
0