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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.
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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. Multiplying by 10
5
0
Moving the decimal point to the right
rewrite one of the terms so that the exponents are equal

2. Indicates the number of times the base is to be multiplied.
1
cube-root key
1. Divide the coefficients 2. Subtract the exponents
exponent

3. To find the square root of any number - simply key in the number (the radicand) and press the
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
Scientific notation
Calculator square-root key
To multiply powers that have the same base:

4. 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
Not
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
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. Multiply the coefficients 2. Add the exponents

5. A number with an exponent of 3 is often said to be
10^1
Engineering notation
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
cubed

6.
Scientific notation
Not
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. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

7. 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
coefficient
you have to adjust the value of the exponent in order avoid changing the actual value.
same exponent
5

8. 1^4 =
Scientific notation
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1
Moving the decimal point to the right

9. A number - when multiplied by itself - is equal to a given number.
square root
When the exponent of a power-of-10 expression is a negative integer:
exponent
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

10. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1
cube root

11. 3^0 =
Are Equal
0
1
decrease the value of the exponent by 1 (dividing by 10)

12. 0^5 =
0
decrease the power-of-10 exponent by the same number of units
decrease the value of the exponent by 1 (dividing by 10)
exponent

13. 0 to any power is equal to
6.74 x 10^-7
decrease the power-of-10 exponent by the same number of units
0
2

14. = 0.1 - or 1 with the decimal point moved one place to the left.
0
10^-1
cube-root key
9 (3^2 = 9)

15. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1. Multiply the coefficients 2. Add the exponents
The solution exists - but not in the real number system.
base

16. 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
same exponent
Because 4 multiplied by itself equals 16.
cube root
cube-root key

17. To multiply powers of ten:
change both terms in order to keep the value the same.
10^2
base
1. Multiply the coefficients 2. Add the exponents

18. 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
0
When moving the decimal point to the left (dividing by 10)

19. Powers of ten can be added or subtracted only when their exponents
Are Equal
decrease the power-of-10 exponent by the same number of units
negative number
6.74 x 10^-7

20. The square root of zero is
1. Divide the coefficients 2. Subtract the exponents
0
Subtract the exponent
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

21. The square of 3 is
Not
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
9 (3^2 = 9)
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. 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.
10^1
1. Divide the coefficients 2. Subtract the exponents
perfect square
To multiply powers that have the same base:

23. Valid powers-of-10 for engineering notation
squared
1
must be multiples of 3 or 0
Not

24. 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
same exponent
move the decimal point the same number of units to the left
1
adjust the value of the coefficient

25. The cube root of zero is
0
must be multiples of 3 or 0
radical sign
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

26. The symbol for the cube root of a number is
2 x 10^9
10^-1
the radical sign with a little 3 that indicates the cube root:
10^2

27. To multiply or divide exponent terms that do not have the same base:
To multiply powers that have the same base:
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
cube root
base

28. Don't bother trying to find the square root of a negative number.
The solution exists - but not in the real number system.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
10^-18
cube root

29. Any number with a negative exponent is equal to
Because 4 multiplied by itself equals 16.
negative number
decrease the power-of-10 exponent by the same number of units
1 divided by that number with a positive exponent

30. Step 1: Add the exponents Step 2: Use the common base
Because 4 multiplied by itself equals 16.
1 divided by that number with a positive exponent
To multiply powers that have the 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

31. 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.
radical sign
When the exponent of a power-of-10 expression is a negative integer:
0
cube-root key

32. To subtract powers of ten:
Same base
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^1
0

33. 1 to any power is equal to
Calculator square-root key
1
Scientific notation
Engineering notation

34. When you move the decimal point in the coefficient to the right
one digit to the left of the decimal point
decrease the power-of-10 exponent by the same number of units
1
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

35. 10 - or 1 with the decimal point moved one place to the right
10^1
1. Multiply the coefficients 2. Add the exponents
you have to adjust the value of the exponent in order avoid changing the actual value.
decrease the value of the exponent by 1 (dividing by 10)

36. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
1
1
cube root
2

37. To add or subtract numbers written with exponents:
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1
exponent

38. Negative cube roots are okay ... negative square roots are
Not
coefficient
0
10^-18

39. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
2 x 10^9
Step 1. Divide the coefficients of the terms

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

41. A number is a second number which - when multiplied by itself three times - equals the original number.
move the decimal point the same number of units to the right
exponent
cube root
a fractional decimal

42. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
move the decimal point the same number of units to the right
proper scientific
must be multiples of 3 or 0
2

43. 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.
cubed
0
Scientific notation
radical sign

44. There are no special rules for adding and subtracting numbers that are written with exponents.
base
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
decrease the value of the exponent by 1 (dividing by 10)

45. 5^1 =
5
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
squared
coefficient

46. 1 to any power is equal to
1. Divide the coefficients 2. Subtract the exponents
1
one digit to the left of the decimal point
0

47. To multiply powers of 10:
When moving the decimal point to the left (dividing by 10)
Step 1. Divide the coefficients of the terms
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.
increase the power-of-10 exponent by the same number of units

48. When moving the decimal point to the right (multiplying by 10)
squared
Same base
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

49. The square root of 9 is
negative number
decrease the power-of-10 exponent by the same number of units
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
3

50. The decimal part
10^1
0
To multiply powers that have the same base:
coefficient