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Test your basic knowledge |

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. The symbol for the cube root of a number is
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
the radical sign with a little 3 that indicates the cube root:
Subtract the exponent
Are Equal

2. 0^5 =
1
0
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Scientific notation

3. To add or subtract numbers written with exponents:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
square root

4. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
Subtract the exponent
2
1
move the decimal point the same number of units to the left

5. A negative exponent does not mean the decimal value is negative. It means the decimal value is
a fractional decimal
1
1
10^1

6.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
decrease the value of the exponent by 1 (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

7. When you move the decimal point in the coefficient to the right
you have to adjust the value of the exponent in order avoid changing the actual value.
decrease the power-of-10 exponent by the same number of units
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
10^-18

8. A number - when multiplied by itself - is equal to a given number.
2
square root
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
base

9. Any number with an exponent of 1 is equal to
When moving the decimal point to the left (dividing by 10)
exponent
itself
radical sign

10. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
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
Subtract the exponent
0
10^-2

11. 10 - or 1 with the decimal point moved one place to the right
square root
a fractional decimal
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

12. Valid powers of 10 for engineering notation are:
The solution exists - but not in the real number system.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
rewrite one of the terms so that the exponents are equal

13. 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
must be multiples of 3 or 0
1
radical sign

14. The square root of 9 is
Scientific notation
3
Same base
1

15. Indicates the number of times the base is to be multiplied.
10^2
5
exponent
a fractional decimal

16. What number multiplied by itself is equal to 16? The answer is 4. Why?
must be multiples of 3 or 0
1
Because 4 multiplied by itself equals 16.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

17. To multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
1
6.74 x 10^-7
square root

18. 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
To multiply powers that have the same base:
0

19. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
cube-root key
2 x 10^9
1

20. = 0.01 - or 1 with the decimal point moved two places to the left.
1
decrease the value of the exponent by 1 (dividing by 10)
10^-2
10^2

21. Scientific notation requires there to be only
a fractional decimal
one digit to the left of the decimal point
square root
move the decimal point the same number of units to the left

22. 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
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. 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 divided by that number with a positive exponent

23. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
radical sign
proper scientific
1
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

24. 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. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
same exponent
move the decimal point the same number of units to the right
Scientific notation

25. Step 1: Add the exponents Step 2: Use the common base
Moving the decimal point to the left
change both terms in order to keep the value the same.
To multiply powers that have the same base:
6.74 x 10^-7

26. 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
3
decrease the power-of-10 exponent by the same number of units
base

27. To find the square root of any number - simply key in the number (the radicand) and press the
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Calculator square-root key
proper scientific
Scientific notation

28. The square of 3 is
0
you have to adjust the value of the exponent in order avoid changing the actual value.
9 (3^2 = 9)
Engineering notation

29. Don't bother trying to find the square root of a negative number.
cube-root key
move the decimal point the same number of units to the right
perfect square
The solution exists - but not in the real number system.

30. To multiply powers of 10:
1
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
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

31. 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
decrease the power-of-10 exponent by the same number of units
change both terms in order to keep the value the same.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1

32. 1^4 =
Not
1 divided by that number with a positive exponent
1
base

33. When you move the decimal point in the coefficient to the left
increase the power-of-10 exponent by the same number of units
1
same exponent
1 divided by that number with a positive exponent

34. Negative cube roots are okay ... negative square roots are
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
adjust the value of the coefficient
Not
Subtract the exponent

35. 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:
must be multiples of 3 or 0
2
Moving the decimal point to the left

36. To add powers of ten:
cubed
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
cube root
Moving the decimal point to the left

37. A very small number such as 0.000000674 can be written with scientific notation as
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
base
6.74 x 10^-7
Because 4 multiplied by itself equals 16.

38. When you decrease the value of the power-of-10 exponent
move the decimal point the same number of units to the right
squared
0
2

39. The cube root of zero is
0
change both terms in order to keep the value the same.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
one digit to the left of the decimal point

40. Valid powers-of-10 for engineering notation
itself
base
0
must be multiples of 3 or 0

41. 1 to any power is equal to
1
0
When the exponent of a power-of-10 expression is a negative integer:
coefficient

42. 1 to any power is equal to
1
squared
adjust the value of the coefficient
base

43. To divide powers that have the same base:
Engineering notation
Moving the decimal point to the right
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
cube root

44. The decimal part
coefficient
9 (3^2 = 9)
5
2

45. There are no special rules for adding and subtracting numbers that are written with exponents.
exponent
5
Subtract the exponent
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

46. Dividing by 10
Moving the decimal point to the left
one digit to the left of the decimal point
must be multiples of 3 or 0
1

47. To divide powers of ten:
1. Divide the coefficients 2. Subtract the exponents
When the exponent of a power-of-10 expression is a negative integer:
increase the power-of-10 exponent by the same number of units
coefficient

48. 0 to any power is equal to
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
0
1 divided by that number with a positive exponent

49. 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.
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
increase the power-of-10 exponent by the same number of units
rewrite one of the terms so that the exponents are equal
perfect square

50. Any number with a negative exponent is equal to
1
proper scientific
1 divided by that number with a positive exponent
The solution exists - but not in the real number system.