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. 0 to any power is equal to
10^-18
0
change both terms in order to keep the value the same.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

2. 100 - or 1 with the decimal point moved two places to the right
move the decimal point the same number of units to the right
10^2
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
To multiply powers that have the same base:

3. 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
Moving the decimal point to the left
Not
coefficient

4. Step 1: Add the exponents Step 2: Use the common base
3
1
To multiply powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

5. 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
9 (3^2 = 9)
Scientific notation
1. Divide the coefficients 2. Subtract the exponents

6. A number with an exponent of 2 is often said to be
squared
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
decrease the value of the exponent by 1 (dividing by 10)
proper scientific

7. The square root of 9 is
square root
10^1
3
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

8. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
square root
increase the power-of-10 exponent by the same number of units
Because 4 multiplied by itself equals 16.
2

9. Represents 1 preceded by 17 zeros and a decimal point.
base
10^1
10^-18
squared

10. Always 10 for scientific notation
you have to adjust the value of the exponent in order avoid changing the actual value.
base
10^-1
Step 1. Divide the coefficients of the terms

11. 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
cube-root key
1. Divide the coefficients 2. Subtract the exponents
2
Moving the decimal point to the left

12. A number with an exponent of 3 is often said to be
cubed
Not
6.74 x 10^-7
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

13. = 0.01 - or 1 with the decimal point moved two places to the left.
1. Multiply the coefficients 2. Add the exponents
10^-2
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
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

14. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
When moving the decimal point to the left (dividing by 10)
proper scientific
1 divided by that number with a positive exponent
6.74 x 10^-7

15. 1 to any power is equal to
proper scientific
2 x 10^9
1
exponent

16. To divide powers that have the same base:
1
decrease the power-of-10 exponent by the same number of units
you have to adjust the value of the exponent in order avoid changing the actual value.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

17. Scientific notation requires there to be only
same exponent
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
3
one digit to the left of the decimal point

18. To multiply powers of ten:
0
1. Multiply the coefficients 2. Add the exponents
cube root
1 divided by that number with a positive exponent

19. 1^4 =
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
To multiply powers that have the same base:
1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

20. 1 to any power is equal to
1
2 x 10^9
cube-root key
10^-18

21. Increase the value of the exponent by 1 (multiplying by 10)
10^1
Engineering notation
When moving the decimal point to the left (dividing by 10)
you have to adjust the value of the exponent in order avoid changing the actual value.

22. Valid powers of 10 for engineering notation are:
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
adjust the value of the coefficient
Because 4 multiplied by itself equals 16.
a fractional decimal

23. Don't bother trying to find the square root of a negative number.
When the exponent of a power-of-10 expression is a negative integer:
0
The solution exists - but not in the real number system.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

24. When you increase the value of the power-of-10 exponent
exponent
move the decimal point the same number of units to the left
When the exponent of a power-of-10 expression is a negative integer:
move the decimal point the same number of units to the right

25. Negative cube roots are okay ... negative square roots are
Not
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Moving the decimal point to the left
cubed

26. When the exponents are not the same
one digit to the left of the decimal point
2 x 10^9
rewrite one of the terms so that the exponents are equal
proper scientific

27. 5^1 =
5
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
To multiply powers that have the same base:
Same base

28. Any number with an exponent of 0 is equal to
1
cubed
3
When the exponent of a power-of-10 expression is a negative integer:

29. 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.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
radical sign
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
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

30. Indicates the number of times the base is to be multiplied.
itself
exponent
radical sign
When moving the decimal point to the left (dividing by 10)

31. A number - when multiplied by itself - is equal to a given number.
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
itself
coefficient
square root

32. The cube root of zero is
proper scientific
same exponent
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
0

33. To multiply powers of 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.
same exponent
exponent
perfect square

34. A number is a second number which - when multiplied by itself three times - equals the original number.
must be multiples of 3 or 0
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
cube root
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

35. 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
cubed
Scientific notation
adjust the value of the coefficient
radical sign

36. The square root of zero is
0
6.74 x 10^-7
must be multiples of 3 or 0
Calculator square-root key

37. 0^5 =
radical sign
10^2
0
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

38. 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.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
squared
Calculator square-root key

39. The cube root of a negative number is also a
cube-root key
move the decimal point the same number of units to the right
negative number
1

40. When you move the decimal point in the coefficient to the right
decrease the power-of-10 exponent by the same number of units
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.
10^1
0

41. When you change the position of the decimal point in a coefficient value
1
exponent
cube root
you have to adjust the value of the exponent in order avoid changing the actual value.

42. Any number with an exponent of 1 is equal to
decrease the power-of-10 exponent by the same number of units
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
itself

43. When moving the decimal point to the right (multiplying by 10)
To multiply powers that have the same base:
decrease the value of the exponent by 1 (dividing by 10)
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
perfect square

44. The symbol for the cube root of a number is
cube-root key
squared
the radical sign with a little 3 that indicates the cube root:
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

45. When you move the decimal point in the coefficient to the left
10^2
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
the radical sign with a little 3 that indicates the cube root:

46. To multiply or divide exponent terms that do not have the same base:
The solution exists - but not in the real number system.
negative number
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^-2

47. To find the square root of any number - simply key in the number (the radicand) and press the
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
Calculator square-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.

48. The decimal part
1
1
coefficient
negative number

49. The square of 3 is
9 (3^2 = 9)
increase the power-of-10 exponent by the same number of units
10^-1
cube root

50. 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
Moving the decimal point to the right
same exponent
0
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.