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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. When the exponents are not the same
negative number
rewrite one of the terms so that the exponents are equal
Engineering notation
base

2. To multiply or divide exponent terms that do not have the same base:
0
Moving the decimal point to the left
1
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

3. A number with an exponent of 3 is often said to be
exponent
cubed
coefficient
Moving the decimal point to the right

4. A number - when multiplied by itself - is equal to a given number.
Engineering 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
one digit to the left of the decimal point
square root

5. 0 to any power is equal to
6.74 x 10^-7
negative number
0
Engineering notation

6. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
Not
2 x 10^9
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
a fractional decimal

7. To multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
Engineering notation
1
Moving the decimal point to the right

8. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
2
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.
The solution exists - but not in the real number system.
decrease the value of the exponent by 1 (dividing by 10)

9. The square of 3 is
Step 1. Divide the coefficients of the terms
Moving the decimal point to the right
9 (3^2 = 9)
1

10. When you change the position of the decimal point in a coefficient value
cubed
squared
5
you have to adjust the value of the exponent in order avoid changing the actual value.

11. The cube root of a negative number is also a
negative number
coefficient
The solution exists - but not in the real number system.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

12. When you move the decimal point in the coefficient to the right
same exponent
decrease the power-of-10 exponent by the same number of units
Engineering notation
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

13. The cube root of zero is
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^-2
1
0

14. 5^1 =
5
must be multiples of 3 or 0
1
perfect square

15. A very small number such as 0.000000674 can be written with scientific notation as
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
6.74 x 10^-7
negative number
0

16. 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.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
increase the power-of-10 exponent by the same number of units
Subtract the exponent

17. Scientific notation requires there to be only
perfect square
0
squared
one digit to the left of the decimal point

18. Dividing by 10
Moving the decimal point to the left
must be multiples of 3 or 0
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1

19. Negative cube roots are okay ... negative square roots are
1
rewrite one of the terms so that the exponents are equal
Not
Subtract the exponent

20. 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 divided by that number with a positive exponent
10^-2
radical sign
proper scientific

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

22. Any number with an exponent of 0 is equal to
6.74 x 10^-7
1. Multiply the coefficients 2. Add the exponents
0
1

23. 0^5 =
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.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
0
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

24. 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.
To multiply powers that have the same base:
move the decimal point the same number of units to the left
perfect square

25. To divide powers of 10:
Step 1. Divide the coefficients of the terms
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
0
Same base

26. Increase the value of the exponent by 1 (multiplying by 10)
Are Equal
one digit to the left of the decimal point
10^-1
When moving the decimal point to the left (dividing by 10)

27. Powers of ten can be added or subtracted only when their exponents
itself
Are Equal
cube-root key
exponent

28. 1 to any power is equal to
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
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1
a fractional decimal

29. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
perfect square
change both terms in order to keep the value the same.
2

30. A negative exponent does not mean the decimal value is negative. It means the decimal value is
a fractional decimal
9 (3^2 = 9)
itself
negative number

31. To subtract powers of ten:
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Not
a fractional decimal

32. To add or subtract numbers written with exponents:
decrease the power-of-10 exponent by the same number of units
The solution exists - but not in the real number system.
1. Multiply the coefficients 2. Add the exponents
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

33. Numbers with exponents can be directly multiplied or divided only when they have the
To multiply powers that have the same base:
Same base
1. Multiply the coefficients 2. Add the exponents
exponent

34. 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.
you have to adjust the value of the exponent in order avoid changing the actual value.
one digit to the left of the 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
When the exponent of a power-of-10 expression is a negative integer:

35. Represents 1 preceded by 17 zeros and a decimal point.
2
Not
When moving the decimal point to the left (dividing by 10)
10^-18

36. 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
itself
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

37. Don't bother trying to find the square root of a negative number.
Moving the decimal point to the left
a fractional decimal
negative number
The solution exists - but not in the real number system.

38. 100 - or 1 with the decimal point moved two places to the right
10^2
10^-2
cube root
10^-1

39. Any number with a negative exponent is equal to
1 divided by that number with a positive exponent
Moving the decimal point to the left
increase the power-of-10 exponent by the same number of units
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

40. Multiplying by 10
Same base
Moving the decimal point to the right
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
must be multiples of 3 or 0

41. = 0.01 - or 1 with the decimal point moved two places to the left.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^-2
5
square root

42. When you decrease the value of the power-of-10 exponent
move the decimal point the same number of units to the right
a fractional decimal
When the exponent of a power-of-10 expression is a negative integer:
10^-18

43. 3^0 =
1
a fractional decimal
base
must be multiples of 3 or 0

44. 1^4 =
1
10^-1
0
Calculator square-root key

45. Step 1: Add the exponents Step 2: Use the common base
cube root
a fractional decimal
2
To multiply powers that have the same base:

46. When you increase the value of the power-of-10 exponent
1
move the decimal point the same number of units to the left
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
cubed

47. What number multiplied by itself is equal to 16? The answer is 4. Why?
Because 4 multiplied by itself equals 16.
adjust the value of the coefficient
same exponent
Engineering notation

48. Any number with an exponent of 1 is equal to
itself
1
you have to adjust the value of the exponent in order avoid changing the actual value.
must be multiples of 3 or 0

49. Always 10 for scientific notation
Calculator square-root key
negative number
base
10^-18

50. To add powers of ten:
1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
cubed
move the decimal point the same number of units to the left