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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. Indicates the number to be multiplied.
base
Scientific notation
1. Multiply the coefficients 2. Add the exponents
Engineering notation

2. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
1 divided by that number with a positive exponent
5
2
Are Equal

3. 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.
10^-1
Engineering notation
decrease the value of the exponent by 1 (dividing by 10)
base

4. To divide powers that have the same base:
Same base
Are Equal
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
coefficient

5. 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
the radical sign with a little 3 that indicates the cube root:
cube-root key
2
6.74 x 10^-7

6. When you move the decimal point in the coefficient to the right
10^1
exponent
rewrite one of the terms so that the exponents are equal
decrease the power-of-10 exponent by the same number of units

7. Step 1: Add the exponents Step 2: Use the common base
To multiply powers that have the same 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
a fractional decimal

8. 1^4 =
1
cube root
9 (3^2 = 9)
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.

9. A number - when multiplied by itself - is equal to a given number.
itself
10^-2
square root
perfect square

10. Any number with an exponent of 0 is equal to
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
1. Divide the coefficients 2. Subtract the exponents
1

11. To find the square root of any number - simply key in the number (the radicand) and press the
1
Scientific notation
Calculator square-root key
1 divided by that number with a positive exponent

12. To add powers of ten:
10^1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Step 1. Divide the coefficients of the terms
base

13. Valid powers of 10 for engineering notation are:
negative number
10^-1
cube root
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

14. The decimal part
6.74 x 10^-7
coefficient
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
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

15. Powers of ten can be added or subtracted only when their exponents
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Are Equal
10^2
Step 1. Divide the coefficients of the terms

16. 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
a fractional decimal
negative number
you have to adjust the value of the exponent in order avoid changing the actual value.
change both terms in order to keep the value the same.

17. A number with an exponent of 3 is often said to be
cubed
Calculator square-root key
0
a fractional decimal

18. Represents 1 preceded by 17 zeros and a decimal point.
1. Divide the coefficients 2. Subtract the exponents
proper scientific
10^-18
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

19. The square of 3 is
Moving the decimal point to the left
1
1. Divide the coefficients 2. Subtract the exponents
9 (3^2 = 9)

20. Don't bother trying to find the square root of a negative number.
itself
The solution exists - but not in the real number system.
2 x 10^9
exponent

21. Always 10 for scientific notation
itself
base
same exponent
10^-1

22. To subtract powers of ten:
Are Equal
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Moving the decimal point to the right
1. Multiply the coefficients 2. Add the exponents

23. The symbol for the cube root of a number is
The solution exists - but not in the real number system.
cube root
proper scientific
the radical sign with a little 3 that indicates the cube root:

24. 0 to any power is equal to
squared
Engineering notation
0
base

25. 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
Calculator square-root key
decrease the value of the exponent by 1 (dividing by 10)
Engineering notation

26. The square root of 9 is
increase the power-of-10 exponent by the same number of units
1. Divide the coefficients 2. Subtract the exponents
3
Subtract the exponent

27. A number is a second number which - when multiplied by itself three times - equals the original number.
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
cube root
1
1

28. Indicates the number of times the base is to be multiplied.
one digit to the left of the decimal point
exponent
10^-1
0

29. When you change the position of the decimal point in a coefficient value
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
decrease the value of the exponent by 1 (dividing by 10)
you have to adjust the value of the exponent in order avoid changing the actual value.

30. Multiplying by 10
Moving the decimal point to the right
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
same exponent

31. What number multiplied by itself is equal to 16? The answer is 4. Why?
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
a fractional decimal
0
Because 4 multiplied by itself equals 16.

32. 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
Scientific notation
3
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

33. Numbers with exponents can be directly multiplied or divided only when they have the
negative number
1
adjust the value of the coefficient
Same base

34.
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
coefficient
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
10^-1

35. 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
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
same exponent
0
decrease the value of the exponent by 1 (dividing by 10)

36. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
2 x 10^9
you have to adjust the value of the exponent in order avoid changing the actual value.
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
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.

37. A negative exponent does not mean the decimal value is negative. It means the decimal value is
a fractional decimal
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. 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

38. The cube root of zero is
base
itself
0
1

39. A very small number such as 0.000000674 can be written with scientific notation as
6.74 x 10^-7
Moving the decimal point to the left
Engineering notation
must be multiples of 3 or 0

40. Scientific notation requires there to be only
Not
1
To multiply powers that have the same base:
one digit to the left of the decimal point

41. 1 to any power is equal to
6.74 x 10^-7
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
1
move the decimal point the same number of units to the left

42. Dividing by 10
coefficient
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
Moving the decimal point to the left

43. To add or subtract numbers written with exponents:
base
cube root
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
3

44. Any number with a negative exponent is equal to
1
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.
1 divided by that number with a positive exponent

45. Any number with an exponent of 1 is equal to
move the decimal point the same number of units to the left
a fractional decimal
exponent
itself

46. Negative cube roots are okay ... negative square roots are
Not
When moving the decimal point to the left (dividing by 10)
9 (3^2 = 9)
decrease the power-of-10 exponent by the same number of units

47. The cube root of a negative number is also a
Scientific notation
negative number
increase the power-of-10 exponent by the same number of units
Because 4 multiplied by itself equals 16.

48. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
exponent
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.
proper scientific
move the decimal point the same number of units to the left

49. 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.
3
Scientific notation
decrease the value of the exponent by 1 (dividing by 10)
1

50. Increase the value of the exponent by 1 (multiplying by 10)
increase the power-of-10 exponent by the same number of units
When moving the decimal point to the left (dividing by 10)
change both terms in order to keep the value the same.
squared