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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. 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
decrease the value of the exponent by 1 (dividing by 10)
0
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

2. Any number with an exponent of 1 is equal to
itself
base
Step 1. Divide the coefficients of the terms
10^-2

3. The cube root of a negative number is also a
negative number
coefficient
perfect square
change both terms in order to keep the value the same.

4. To add or subtract numbers written with exponents:
5
Not
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
6.74 x 10^-7

5. 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.
6.74 x 10^-7
2 x 10^9
radical sign
10^-2

6. Valid powers-of-10 for engineering notation
6.74 x 10^-7
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. Divide the coefficients 2. Subtract the exponents

7. When you change the position of the decimal point in a coefficient value
you have to adjust the value of the exponent in order avoid changing the actual value.
10^2
increase the power-of-10 exponent by the same number of units
Are Equal

8. 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
1
10^-1
decrease the power-of-10 exponent by the same number of units

9. When you move the decimal point in the coefficient to the left
To multiply powers that have the same base:
increase the power-of-10 exponent by the same number of units
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

10. The cube root of zero is
1
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
move the decimal point the same number of units to the right
0

11. A number with an exponent of 3 is often said to be
1
one digit to the left of the decimal point
cubed
Step 1. Divide the coefficients of the terms

12. When you increase the value of the power-of-10 exponent
move the decimal point the same number of units to the left
2 x 10^9
0
one digit to the left of the decimal point

13. 10 - or 1 with the decimal point moved one place to the right
negative number
10^1
decrease the value of the exponent by 1 (dividing by 10)
you have to adjust the value of the exponent in order avoid changing the actual value.

14. 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
you have to adjust the value of the exponent in order avoid changing the actual value.
Moving the decimal point to the right
Not
adjust the value of the coefficient

15. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
proper scientific
base
a fractional decimal

16. 3^0 =
When the exponent of a power-of-10 expression is a negative integer:
rewrite one of the terms so that the exponents are equal
itself
1

17. 1^4 =
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1
Scientific notation
2

18. 5^1 =
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
When moving the decimal point to the left (dividing by 10)
5
itself

19. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
9 (3^2 = 9)
2
When moving the decimal point to the left (dividing by 10)
10^-2

20. What number multiplied by itself is equal to 16? The answer is 4. Why?
move the decimal point the same number of units to the left
Calculator square-root key
Moving the decimal point to the right
Because 4 multiplied by itself equals 16.

21. The decimal part
coefficient
cube root
rewrite one of the terms so that the exponents are equal
exponent

22. A very small number such as 0.000000674 can be written with scientific notation as
1
rewrite one of the terms so that the exponents are equal
6.74 x 10^-7
5

23. 0 to any power is equal to
cubed
0
Are Equal
10^1

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.
10^-2
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
perfect square
you have to adjust the value of the exponent in order avoid changing the actual value.

25. When you decrease the value of the power-of-10 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.
exponent
cubed
move the decimal point the same number of units to the right

26. Scientific notation requires there to be only
10^-2
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
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

27. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Moving the decimal point to the right
Same base

28.
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
rewrite one of the terms so that the exponents are equal
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
0

29. A negative exponent does not mean the decimal value is negative. It means the decimal value is
radical sign
a fractional decimal
1 divided by that number with a positive exponent
cube root

30. 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
The solution exists - but not in the real number system.
base
must be multiples of 3 or 0

31. Always 10 for scientific notation
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.
square root
adjust the value of the coefficient

32. 100 - or 1 with the decimal point moved two places to the right
2
10^2
Not
0

33. When the exponents are not the same
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
cube root
1 divided by that number with a positive exponent
rewrite one of the terms so that the exponents are equal

34. Numbers with exponents can be directly multiplied or divided only when they have the
10^2
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
Same base

35. 1 to any power is equal to
10^-18
1
same exponent
10^2

36. Represents 1 preceded by 17 zeros and a decimal point.
square root
1
1 divided by that number with a positive exponent
10^-18

37. 0^5 =
2
one digit to the left of the decimal point
0
1

38. For the 10
exponent
10^-2
Moving the decimal point to the right
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.

39. 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
To multiply powers that have the same base:
cube-root key
itself
Not

40. A number is a second number which - when multiplied by itself three times - equals the original number.
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
The solution exists - but not in the real number system.
Calculator square-root key
cube root

41. The symbol for the cube root of a number is
decrease the power-of-10 exponent by the same number of units
1
10^-18
the radical sign with a little 3 that indicates the cube root:

42. A number with an exponent of 2 is often said to be
squared
must be multiples of 3 or 0
10^2
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

43. There are no special rules for adding and subtracting numbers that are written with exponents.
decrease the power-of-10 exponent by the same number of units
10^-18
1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

44. A number - when multiplied by itself - is equal to a given number.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
3
square root
0

45. To subtract powers of ten:
2 x 10^9
the radical sign with a little 3 that indicates the cube root:
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)

46. Indicates the number to be multiplied.
base
10^-1
0
itself

47. The square of 3 is
0
9 (3^2 = 9)
negative number
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

48. 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
base
When the exponent of a power-of-10 expression is a negative integer:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
change both terms in order to keep the value the same.

49. 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.
1. Multiply the coefficients 2. Add the exponents
0
3
Engineering notation

50. When moving the decimal point to the right (multiplying by 10)
Moving the decimal point to the right
decrease the value of the exponent by 1 (dividing by 10)
must be multiples of 3 or 0
rewrite one of the terms so that the exponents are equal