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CLEP General Mathematics: Powers Exponents And Roots

Subjects : clep, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. 1 to any power is equal to
base
Calculator square-root key
Not
1

2. Numbers with exponents can be directly multiplied or divided only when they have the
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
cube root
Step 1. Divide the coefficients of the terms
Same base

3. 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.
When moving the decimal point to the left (dividing by 10)
1
negative number
perfect square

4. Any number with a negative exponent is equal to
1 divided by that number with a positive exponent
Scientific notation
decrease the power-of-10 exponent by the same number of units
10^-1

5. To multiply or divide exponent terms that do not have the same base:
When moving the decimal point to the left (dividing by 10)
increase the power-of-10 exponent by the same number of units
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 left

6. Any number with an exponent of 1 is equal to
itself
Because 4 multiplied by itself equals 16.
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
10^-1

7. = 0.1 - or 1 with the decimal point moved one place to the left.
10^-1
1
Moving the decimal point to the right
one digit to the left of the decimal point

8. Indicates the number to be multiplied.
base
1
Moving the decimal point to the right
perfect square

9. When you increase the value of the power-of-10 exponent
cube-root key
increase the power-of-10 exponent by the same number of units
one digit to the left of the decimal point
move the decimal point the same number of units to the left

10. 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
move the decimal point the same number of units to the right
1. Divide the coefficients 2. Subtract the exponents
10^2

11. 3^0 =
1. Divide the coefficients 2. Subtract the exponents
When moving the decimal point to the left (dividing by 10)
The solution exists - but not in the real number system.
1

12. 0^5 =
0
10^2
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
Moving the decimal point to the left

13. = 0.01 - or 1 with the decimal point moved two places to the left.
rewrite one of the terms so that the exponents are equal
1. Multiply the coefficients 2. Add the exponents
Not
10^-2

14. Step 1: Add the exponents Step 2: Use the common base
square root
Calculator square-root key
To multiply powers that have the same base:
1. Divide the coefficients 2. Subtract the exponents

15. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
exponent
proper scientific
cubed
1. Multiply the coefficients 2. Add the exponents

16. When you decrease the value of the power-of-10 exponent
cube-root key
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
exponent

17. 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
coefficient
must be multiples of 3 or 0
proper scientific
change both terms in order to keep the value the same.

18. To divide powers of 10:
squared
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Step 1. Divide the coefficients of the terms
10^-2

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

20. When moving the decimal point to the right (multiplying by 10)
decrease the value of the exponent by 1 (dividing by 10)
When moving the decimal point to the left (dividing by 10)
change both terms in order to keep the value the same.
same exponent

21. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
0
Engineering notation
Calculator square-root key

22. The decimal part
coefficient
Scientific notation
a fractional decimal
perfect square

23. Powers of ten can be added or subtracted only when their exponents
1
Are Equal
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
2 x 10^9

24. Scientific notation requires there to be only
0
one digit to the left of the decimal point
proper scientific
exponent

25. 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
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
When moving the decimal point to the left (dividing by 10)

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

27. Always 10 for scientific notation
Engineering notation
base
1. Multiply the coefficients 2. Add the exponents
0

28. To add powers of ten:
1. Divide the coefficients 2. Subtract the exponents
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. 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.

29. The symbol for the cube root of a number is
10^-18
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
exponent
the radical sign with a little 3 that indicates the cube root:

30.
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
10^-1
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.

31. To find the square root of any number - simply key in the number (the radicand) and press the
Calculator square-root key
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
The solution exists - but not in the real number system.
10^1

32. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
negative number
radical sign
same exponent

33. 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:
you have to adjust the value of the exponent in order avoid changing the actual value.
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

34. Any number with an exponent of 0 is equal to
Not
square root
perfect square
1

35. 1^4 =
Same base
a fractional decimal
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
1

36. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
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
1 divided by that number with a positive exponent
10^-2

37. A negative exponent does not mean the decimal value is negative. It means the decimal value is
decrease the value of the exponent by 1 (dividing by 10)
a fractional decimal
Are Equal
move the decimal point the same number of units to the right

38. To divide powers of ten:
coefficient
1. Divide the coefficients 2. Subtract the exponents
proper scientific
adjust the value of the coefficient

39. Multiplying by 10
0
must be multiples of 3 or 0
radical sign
Moving the decimal point to the right

40. 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.
1
1
10^-2
Scientific notation

41. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
1
2
1

42. To multiply powers of 10:
decrease the value of the exponent by 1 (dividing by 10)
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.
10^-2
Moving the decimal point to the left

43. Valid powers of 10 for engineering notation are:
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
0
you have to adjust the value of the exponent in order avoid changing the actual value.

44. The square root of 9 is
perfect square
10^-18
0
3

45. There are no special rules for adding and subtracting numbers that are written with exponents.
1
1 divided by that number with a positive exponent
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
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

46. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
perfect square
a fractional decimal
The solution exists - but not in the real number system.
Subtract the exponent

47. A number with an exponent of 2 is often said to be
Step 1. Divide the coefficients of the terms
1
squared
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

48. The cube root of zero is
cubed
Engineering notation
10^2
0

49. To divide powers that have the same base:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
one digit to the left of the decimal point
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

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