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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. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
rewrite one of the terms so that the exponents are equal
The solution exists - but not in the real number system.
6.74 x 10^-7
Subtract the exponent

2. Negative cube roots are okay ... negative square roots are
Not
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.
rewrite one of the terms so that the exponents are equal
square root

3. A number with an exponent of 2 is often said to be
squared
Moving the decimal point to the left
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

4. A number is a second number which - when multiplied by itself three times - equals the original number.
negative number
10^-18
same exponent
cube root

5. 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.
Scientific notation
move the decimal point the same number of units to the left
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
negative number

6. When you increase the value of the power-of-10 exponent
To multiply powers that have the same base:
move the decimal point the same number of units to the left
Engineering notation
1

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
same exponent
2 x 10^9
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.
move the decimal point the same number of units to the right

8. For the 10
decrease the power-of-10 exponent by the same number of units
a fractional decimal
1. Multiply the coefficients 2. Add the exponents
exponent

9. To add or subtract numbers written with exponents:
exponent
10^2
0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

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

11. Always 10 for scientific notation
cubed
base
Moving the decimal point to the left
6.74 x 10^-7

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

13. To find the square root of any number - simply key in the number (the radicand) and press the
9 (3^2 = 9)
0
Calculator square-root key
Moving the decimal point to the left

14. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
proper scientific
cube root
itself
10^-18

15. 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
adjust the value of the coefficient
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
6.74 x 10^-7
Subtract the exponent

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
move the decimal point the same number of units to the right
base
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
cube-root key

17. The square of 3 is
squared
move the decimal point the same number of units to the left
1
9 (3^2 = 9)

18. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
10^-18
2 x 10^9
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
base

19. 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.
Moving the decimal point to the right
radical sign
perfect square
0

20. What number multiplied by itself is equal to 16? The answer is 4. Why?
Step 1. Divide the coefficients of the terms
squared
Because 4 multiplied by itself equals 16.
Engineering notation

21. 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.
same exponent
3
perfect square
To multiply powers that have the same base:

22. 0^5 =
0
10^-18
6.74 x 10^-7
cube root

23. When moving the decimal point to the right (multiplying by 10)
10^-18
increase the power-of-10 exponent by the same number of units
Moving the decimal point to the right
decrease the value of the exponent by 1 (dividing by 10)

24. 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.
same exponent
negative number
Engineering notation
10^-2

25. The square root of 9 is
same exponent
10^-1
3
must be multiples of 3 or 0

26. To multiply powers of ten:
1
1. Multiply the coefficients 2. Add the exponents
3
0

27. 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
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
move the decimal point the same number of units to the right
rewrite one of the terms so that the exponents are equal

28. A number with an exponent of 3 is often said to be
cubed
the radical sign with a little 3 that indicates the cube root:
adjust the value of the coefficient
1

29. When you move the decimal point in the coefficient to the left
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
you have to adjust the value of the exponent in order avoid changing the actual value.
increase the power-of-10 exponent by the same number of units
10^2

30. To divide powers of 10:
Step 1. Divide the coefficients of the terms
change both terms in order to keep the value the same.
1
3

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.
When the exponent of a power-of-10 expression is a negative integer:
1
Scientific notation
negative number

32. Don't bother trying to find the square root of a negative number.
decrease the value of the exponent by 1 (dividing by 10)
Moving the decimal point to the left
The solution exists - but not in the real number system.
increase the power-of-10 exponent by the same number of units

33. Powers of ten can be added or subtracted only when their exponents
Are Equal
cube root
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. 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.

34. Represents 1 preceded by 17 zeros and a decimal point.
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.
base
10^-18
radical sign

35. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
The solution exists - but not in the real number system.
5
rewrite one of the terms so that the exponents are equal

36. Dividing by 10
exponent
Moving the decimal point to the left
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

37. Step 1: Add the exponents Step 2: Use the common base
increase the power-of-10 exponent by the same number of units
To multiply powers that have the same base:
Are Equal
The solution exists - but not in the real number system.

38. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
2
increase the power-of-10 exponent by the same number of units
Scientific notation
3

39. 0 to any power is equal to
Engineering notation
1 divided by that number with a positive exponent
0
Because 4 multiplied by itself equals 16.

40. Any number with an exponent of 0 is equal to
base
10^1
1. Divide the coefficients 2. Subtract the exponents
1

41. A negative exponent does not mean the decimal value is negative. It means the decimal value is
cubed
1. Divide the coefficients 2. Subtract the exponents
a fractional decimal
same exponent

42.
6.74 x 10^-7
exponent
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

43. When you decrease the value of the power-of-10 exponent
Because 4 multiplied by itself equals 16.
negative number
move the decimal point the same number of units to the right
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

44. Multiplying by 10
Moving the decimal point to the right
Engineering notation
1. Multiply the coefficients 2. Add the exponents
squared

45. Valid powers of 10 for engineering notation are:
base
adjust the value of the coefficient
Are Equal
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

46. Any number with an exponent of 1 is equal to
itself
1. Divide the coefficients 2. Subtract the exponents
Because 4 multiplied by itself equals 16.
5

47. 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
change both terms in order to keep the value the same.
squared
1
0

48. To subtract powers of ten:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
base
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

49. 1^4 =
cube root
1
adjust the value of the coefficient
The solution exists - but not in the real number system.

50. To add powers of ten:
3
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
perfect square
1