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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. 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
Step 1. Divide the coefficients of the terms
cube-root key
Subtract the exponent
9 (3^2 = 9)

2. Scientific notation requires there to be only
Calculator square-root key
3
one digit to the left of the decimal point
proper scientific

3. 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.
3
When the exponent of a power-of-10 expression is a negative integer:
the radical sign with a little 3 that indicates the cube root:
Moving the decimal point to the right

4. Don't bother trying to find the square root of a negative number.
The solution exists - but not in the real number system.
increase the power-of-10 exponent by the same number of units
1
0

5. There are no special rules for adding and subtracting numbers that are written with exponents.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
decrease the value of the exponent by 1 (dividing by 10)
1
Not

6. To divide powers of 10:
Step 1. Divide the coefficients of the terms
1. Divide the coefficients 2. Subtract the exponents
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

7. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
proper scientific
10^-18
exponent
To multiply powers that have the same base:

8. Multiplying by 10
must be multiples of 3 or 0
Moving the decimal point to the right
When moving the decimal point to the left (dividing by 10)
1

9. The square root of zero is
0
Not
square root
rewrite one of the terms so that the exponents are equal

10. 5^1 =
move the decimal point the same number of units to the right
Same base
0
5

11. = 0.1 - or 1 with the decimal point moved one place to the left.
Step 1. Divide the coefficients of the terms
10^-1
1
coefficient

12. Numbers with exponents can be directly multiplied or divided only when they have the
must be multiples of 3 or 0
Same base
a fractional decimal
0

13. 1^4 =
1
Step 1. Divide the coefficients of the terms
decrease the power-of-10 exponent by the same number of units
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

14. 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
cube-root key
change both terms in order to keep the value the same.
Subtract the exponent
rewrite one of the terms so that the exponents are equal

15. Always 10 for scientific notation
1
base
move the decimal point the same number of units to the right
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

16. A number is a second number which - when multiplied by itself three times - equals the original number.
coefficient
cube root
Moving the decimal point 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

17. A number - when multiplied by itself - is equal to a given number.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
square root
Are Equal
cube-root key

18. 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.
radical sign
base
10^-2
you have to adjust the value of the exponent in order avoid changing the actual value.

19. To multiply powers of 10:
square root
Moving the decimal point to the left
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

20. What number multiplied by itself is equal to 16? The answer is 4. Why?
change both terms in order to keep the value the same.
Moving the decimal point to the right
cube-root key
Because 4 multiplied by itself equals 16.

21. A number with an exponent of 3 is often said to be
rewrite one of the terms so that the exponents are equal
decrease the value of the exponent by 1 (dividing by 10)
cubed
1

22. Any number with a negative exponent is equal to
Subtract the exponent
1
9 (3^2 = 9)
1 divided by that number with a positive exponent

23. When you increase the value of the power-of-10 exponent
Engineering notation
move the decimal point the same number of units to the left
increase the power-of-10 exponent by the same number of units
coefficient

24. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
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
adjust the value of the coefficient

25. Valid powers of 10 for engineering notation are:
6.74 x 10^-7
rewrite one of the terms so that the exponents are equal
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

26. To add or subtract numbers written with exponents:
squared
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.
same exponent

27. 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.
negative number
Engineering notation
10^-18
6.74 x 10^-7

28. 1 to any power is equal to
0
1
increase the power-of-10 exponent by the same number of units
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

29. To multiply or divide exponent terms that do not have the same base:
When the exponent of a power-of-10 expression is a negative integer:
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
rewrite one of the terms so that the exponents are equal
Not

30. Increase the value of the exponent by 1 (multiplying by 10)
When moving the decimal point to the left (dividing by 10)
proper scientific
Step 1. Divide the coefficients of the terms
the radical sign with a little 3 that indicates the cube root:

31. 100 - or 1 with the decimal point moved two places to the right
3
Moving the decimal point to the right
10^2
6.74 x 10^-7

32. 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.
coefficient
Same base
decrease the value of the exponent by 1 (dividing by 10)

33. Dividing by 10
1
0
Moving the decimal point to the left
exponent

34. A negative exponent does not mean the decimal value is negative. It means the decimal value is
radical sign
cubed
a fractional decimal
Same base

35. To find the square root of any number - simply key in the number (the radicand) and press the
move the decimal point the same number of units to the left
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Subtract the exponent
Calculator square-root key

36. Indicates the number to be multiplied.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
exponent
radical sign
base

37. The square of 3 is
10^1
Moving the decimal point to the right
square root
9 (3^2 = 9)

38. When you decrease the value of the power-of-10 exponent
Because 4 multiplied by itself equals 16.
1
move the decimal point the same number of units to the right
the radical sign with a little 3 that indicates the cube root:

39. The square root of 9 is
squared
must be multiples of 3 or 0
3
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

40. = 0.01 - or 1 with the decimal point moved two places 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
The solution exists - but not in the real number system.
10^-2
a fractional decimal

41. When moving the decimal point to the right (multiplying by 10)
perfect square
decrease the value of the exponent by 1 (dividing by 10)
base
0

42. To subtract powers of ten:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Are Equal
a fractional decimal
Engineering notation

43. 0^5 =
Moving the decimal point to the left
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
must be multiples of 3 or 0
0

44. Valid powers-of-10 for engineering notation
must be multiples of 3 or 0
proper scientific
1 divided by that number with a positive exponent
decrease the value of the exponent by 1 (dividing by 10)

45. 1 to any power is equal to
0
1 divided by that number with a positive exponent
1
1. Multiply the coefficients 2. Add the exponents

46. Any number with an exponent of 1 is equal to
exponent
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
When the exponent of a power-of-10 expression is a negative integer:

47. Step 1: Add the exponents Step 2: Use the common base
The solution exists - but not in the real number system.
To multiply powers that have the same base:
one digit to the left of the decimal point
base

48. 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.
decrease the value of the exponent by 1 (dividing by 10)
Scientific notation
1
square root

49. 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
exponent
adjust the value of the coefficient
0
Engineering notation

50. The decimal part
exponent
coefficient
proper scientific
square root