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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. The square root of 9 is
10^2
decrease the value of the exponent by 1 (dividing by 10)
3
10^-2

2. 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
1
Subtract the exponent
exponent

3. To find the square root of any number - simply key in the number (the radicand) and press the
Because 4 multiplied by itself equals 16.
Calculator square-root key
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
move the decimal point the same number of units to the right

4. To add 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
Because 4 multiplied by itself equals 16.
1. Divide the coefficients 2. Subtract the exponents
decrease the value of the exponent by 1 (dividing by 10)

5. Negative cube roots are okay ... negative square roots are
Same base
move the decimal point the same number of units to the right
Not
Engineering notation

6. 1 to any power is equal to
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
square root
Calculator square-root key
1

7. To multiply powers of 10:
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. Subtract the exponents (divisor from dividend) Step 2. Use the common base
cube root
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.

8. 0^5 =
negative number
10^-2
10^-18
0

9. = 0.1 - or 1 with the decimal point moved one place to the left.
Calculator square-root key
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1. Multiply the coefficients 2. Add the exponents
10^-1

10. Multiplying by 10
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Moving the decimal point to the right
When moving the decimal point to the left (dividing by 10)
Because 4 multiplied by itself equals 16.

11. The symbol for the cube root of a number is
6.74 x 10^-7
Subtract the exponent
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

12. 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
1
2 x 10^9
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
cube-root key

13. 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
you have to adjust the value of the exponent in order avoid changing the actual value.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
same exponent
0

14. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
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
Subtract the exponent

15. To multiply or divide exponent terms that do not have the same base:
Same base
2
10^2
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

16. To divide powers that have the same base:
Not
the radical sign with a little 3 that indicates the cube root:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
must be multiples of 3 or 0

17. When you increase the value of the power-of-10 exponent
0
Are Equal
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
move the decimal point the same number of units to the left

18. Any number with a negative exponent is equal to
When the exponent of a power-of-10 expression is a negative integer:
decrease the value of the exponent by 1 (dividing by 10)
When moving the decimal point to the left (dividing by 10)
1 divided by that number with a positive exponent

19. 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.
Moving the decimal point to the left
1
The solution exists - but not in the real number system.
Engineering notation

20. The square root of zero is
Step 1. Divide the coefficients of the terms
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
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

21. To multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
move the decimal point the same number of units to the right
10^1
Calculator square-root key

22. 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
cube root
Moving the decimal point to the right
squared

23. The decimal part
squared
coefficient
1
10^1

24. A number - when multiplied by itself - is equal to a given number.
squared
10^-18
1
square root

25. When you decrease the value of the power-of-10 exponent
move the decimal point the same number of units to the right
the radical sign with a little 3 that indicates the cube root:
base
coefficient

26. Step 1: Add the exponents Step 2: Use the common 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.
10^1
1. Multiply the coefficients 2. Add the exponents

27.
perfect square
Are Equal
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

28. When you change the position of the decimal point in a coefficient value
perfect square
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1. Multiply the coefficients 2. Add the exponents
you have to adjust the value of the exponent in order avoid changing the actual value.

29. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
1
1. Divide the coefficients 2. Subtract the exponents
proper scientific
Engineering notation

30. 1^4 =
1
Engineering notation
2 x 10^9
proper scientific

31. The cube root of a negative number is also a
Moving the decimal point to the left
10^-1
Because 4 multiplied by itself equals 16.
negative number

32. Powers of ten can be added or subtracted only when their exponents
Are Equal
base
move the decimal point the same number of units to the right
Because 4 multiplied by itself equals 16.

33. What number multiplied by itself is equal to 16? The answer is 4. Why?
10^-2
itself
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
Because 4 multiplied by itself equals 16.

34. To add or subtract numbers written with exponents:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the left
Because 4 multiplied by itself equals 16.
1. Multiply the coefficients 2. Add the exponents

35. Any number with an exponent of 0 is equal to
base
0
To multiply powers that have the same base:
1

36. Don't bother trying to find the square root of a negative number.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
The solution exists - but not in the real number system.
2
cubed

37. A number with an exponent of 2 is often said to be
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.
0
squared

38. Numbers with exponents can be directly multiplied or divided only when they have the
increase the power-of-10 exponent by the same number of units
decrease the value of the exponent by 1 (dividing by 10)
5
Same base

39. The square of 3 is
10^1
9 (3^2 = 9)
2
move the decimal point the same number of units to the right

40. A very small number such as 0.000000674 can be written with scientific notation as
5
1
6.74 x 10^-7
Calculator square-root key

41. For the 10
exponent
Step 1. Divide the coefficients of the terms
the radical sign with a little 3 that indicates the cube root:
you have to adjust the value of the exponent in order avoid changing the actual value.

42. 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
Moving the decimal point to the left
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
change both terms in order to keep the value the same.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

43. 10 - or 1 with the decimal point moved one place to the right
10^2
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^1
When moving the decimal point to the left (dividing by 10)

44. 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:
10^-18
base
coefficient

45. There are no special rules for adding and subtracting numbers that are written with exponents.
same exponent
2 x 10^9
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
square root

46. 1 to any power is equal to
The solution exists - but not in the real number system.
3
Calculator square-root key
1

47. 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
cube-root key
1
increase the power-of-10 exponent by the same number of units

48. A number with an exponent of 3 is often said to be
you have to adjust the value of the exponent in order avoid changing the actual value.
cubed
negative number
change both terms in order to keep the value the same.

49. 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 moving the decimal point to the left (dividing by 10)
The solution exists - but not in the real number system.
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

50. A number is a second number which - when multiplied by itself three times - equals the original number.
Moving the decimal point to the left
10^-1
move the decimal point the same number of units to the right
cube root