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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. 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
cubed
exponent
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
change both terms in order to keep the value the same.

2. 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
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
a fractional decimal

3. 1 to any power is equal to
1
1. Divide the coefficients 2. Subtract the exponents
0
Same base

4. When the exponents are not the same
5
rewrite one of the terms so that the exponents are equal
must be multiples of 3 or 0
exponent

5. When you move the decimal point in the coefficient to the left
Are Equal
increase the power-of-10 exponent by the same number of units
10^2
exponent

6. To divide powers of 10:
must be multiples of 3 or 0
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Step 1. Divide the coefficients of the terms
1

7. To multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
The solution exists - but not in the real number system.
0
base

8. 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
Subtract the 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.
1

9. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Engineering notation
1. Multiply the coefficients 2. Add the exponents
squared

10. Always 10 for scientific notation
base
Subtract the exponent
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
The solution exists - but not in the real number system.

11. To divide powers of ten:
squared
When moving the decimal point to the left (dividing by 10)
1. Divide the coefficients 2. Subtract the exponents
10^-18

12. 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.
Subtract the exponent
0
6.74 x 10^-7

13. Valid powers of 10 for engineering notation are:
base
decrease the value of the exponent by 1 (dividing by 10)
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
10^-2

14. To add or subtract numbers written with exponents:
cube root
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
negative number
Same base

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

16.
9 (3^2 = 9)
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
you have to adjust the value of the exponent in order avoid changing the actual value.
Are Equal

17. The cube root of zero is
0
increase the power-of-10 exponent by the same number of units
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
a fractional decimal

18. Step 1: Add the exponents Step 2: Use the common base
itself
When the exponent of a power-of-10 expression is a negative integer:
10^-2
To multiply powers that have the same base:

19. A number - when multiplied by itself - is equal to a given number.
Step 1. Divide the coefficients of the terms
decrease the value of the exponent by 1 (dividing by 10)
square root
To multiply powers that have the same base:

20. 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
rewrite one of the terms so that the exponents are equal
perfect square
cube-root key
one digit to the left of the decimal point

21. When you increase the value of the power-of-10 exponent
rewrite one of the terms so that the exponents are equal
move the decimal point the same number of units to the left
The solution exists - but not in the real number system.
2

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.
perfect square
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
cube root
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

23. Negative cube roots are okay ... negative square roots are
6.74 x 10^-7
0
1
Not

24. 0^5 =
Are Equal
0
1. Multiply the coefficients 2. Add the exponents
9 (3^2 = 9)

25. = 0.1 - or 1 with the decimal point moved one place to the left.
coefficient
10^-1
base
Scientific notation

26. 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
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
cube-root key

27. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
0
you have to adjust the value of the exponent in order avoid changing the actual value.
Engineering notation

28. 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
0
same exponent
10^-1
adjust the value of the coefficient

29. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
proper scientific
the radical sign with a little 3 that indicates the cube root:
exponent
10^2

30. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Subtract the exponent
move the decimal point the same number of units to the left
0

31. Numbers with exponents can be directly multiplied or divided only when they have the
same exponent
Scientific notation
Same base
one digit to the left of the decimal point

32. The symbol for the cube root of a number is
one digit to the left of the decimal point
radical sign
the radical sign with a little 3 that indicates the cube root:
a fractional decimal

33. A number with an exponent of 2 is often said to be
squared
1
Engineering notation
must be multiples of 3 or 0

34. The decimal part
cubed
coefficient
Scientific notation
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

35. Valid powers-of-10 for engineering notation
you have to adjust the value of the exponent in order avoid changing the actual value.
3
must be multiples of 3 or 0
9 (3^2 = 9)

36. 1 to any power is equal to
Calculator square-root key
5
1
1. Multiply the coefficients 2. Add the exponents

37. When you decrease the value of the power-of-10 exponent
1. Divide the coefficients 2. Subtract the exponents
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
move the decimal point the same number of units to the right

38. The square of 3 is
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
9 (3^2 = 9)
move the decimal point the same number of units to the right
proper scientific

39. Dividing by 10
squared
itself
Moving the decimal point to the left
6.74 x 10^-7

40. Powers of ten can be added or subtracted only when their exponents
0
itself
Are Equal
proper scientific

41. 0 to any power is equal to
5
Moving the decimal point to the right
Scientific notation
0

42. Don't bother trying to find the square root of a negative number.
Moving the decimal point to the right
The solution exists - but not in the real number system.
itself
1. Multiply the coefficients 2. Add the exponents

43. To add powers of ten:
1. Divide the coefficients 2. Subtract the exponents
0
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
decrease the value of the exponent by 1 (dividing by 10)

44. A number with an exponent of 3 is often said to be
cubed
Same base
exponent
1

45. When you move the decimal point in the coefficient to the right
decrease the power-of-10 exponent by the same number of units
rewrite one of the terms so that the exponents are equal
2 x 10^9
one digit to the left of the decimal point

46. There are no special rules for adding and subtracting numbers that are written with exponents.
1 divided by that number with a positive exponent
you have to adjust the value of the exponent in order avoid changing the actual value.
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.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

47. 10 - or 1 with the decimal point moved one place to the right
When moving the decimal point to the left (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
5
10^1

48. A number is a second number which - when multiplied by itself three times - equals the original number.
0
1 divided by that number with a positive exponent
cube root
3

49. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
2
1. Divide the coefficients 2. Subtract the exponents
0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

50. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
one digit to the left of the decimal point
1. Divide the coefficients 2. Subtract the exponents
The solution exists - but not in the real number system.
2 x 10^9