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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.
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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. A number is a second number which - when multiplied by itself three times - equals the original number.
Engineering notation
cube root
cubed
1. Divide the coefficients 2. Subtract the exponents

2. The cube root of a negative number is also a
10^1
Moving the decimal point to the right
squared
negative number

3. Always 10 for scientific notation
Moving the decimal point to the left
square root
base
1 divided by that number with a positive exponent

4. Increase the value of the exponent by 1 (multiplying by 10)
radical sign
same exponent
2
When moving the decimal point to the left (dividing by 10)

5. 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.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
coefficient
base
perfect square

6. 0^5 =
0
1. Multiply the coefficients 2. Add the exponents
5
10^-1

7. To multiply powers of ten:
decrease the value of the exponent by 1 (dividing by 10)
1. Multiply the coefficients 2. Add the exponents
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
9 (3^2 = 9)

8. When you move the decimal point in the coefficient to the left
Engineering notation
Same base
increase the power-of-10 exponent by the same number of units
1

9. Valid powers of 10 for engineering notation are:
increase the power-of-10 exponent by the same number of units
2 x 10^9
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
square root

10. To add or subtract numbers written with exponents:
1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
radical sign

11. The square root of 9 is
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
3
To multiply powers that have the same base:

12. Negative cube roots are okay ... negative square roots are
2
Not
base
rewrite one of the terms so that the exponents are equal

13. Any number with a negative exponent is equal to
move the decimal point the same number of units to the right
The solution exists - but not in the real number system.
3
1 divided by that number with a positive exponent

14. 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.
Same base
Moving the decimal point to the left
exponent
Scientific notation

15. When you change the position of the decimal point in a coefficient value
10^1
6.74 x 10^-7
Are Equal
you have to adjust the value of the exponent in order avoid changing the actual value.

16. Step 1: Add the exponents Step 2: Use the common base
rewrite one of the terms so that the exponents are equal
The solution exists - but not in the real number system.
To multiply powers that have the same base:
itself

17. A number - when multiplied by itself - is equal to a given number.
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
must be multiples of 3 or 0
square root
1

18. A very small number such as 0.000000674 can be written with scientific notation as
adjust the value of the coefficient
6.74 x 10^-7
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
Engineering notation

19. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
proper scientific
10^1
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
1. Multiply the coefficients 2. Add the exponents

20. For the 10
increase the power-of-10 exponent by the same number of units
1
exponent
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

21. To add powers of ten:
1
decrease the value of the exponent by 1 (dividing by 10)
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
adjust the value of the coefficient

22. To divide powers of 10:
Not
decrease the power-of-10 exponent by the same number of units
Step 1. Divide the coefficients of the terms
perfect square

23. = 0.1 - or 1 with the decimal point moved one place to the left.
The solution exists - but not in the real number system.
10^-1
0
change both terms in order to keep the value the same.

24. Indicates the number of times the base is to be multiplied.
must be multiples of 3 or 0
6.74 x 10^-7
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
exponent

25. Dividing by 10
Moving the decimal point to the left
To multiply powers that have the same base:
Scientific notation
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.

26. 0 to any power is equal to
perfect square
Are Equal
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
0

27. To divide powers that have the same base:
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
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
change both terms in order to keep the value the same.

28. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
1. Divide the coefficients 2. Subtract the exponents
2
adjust the value of the coefficient
Subtract the exponent

29. 1^4 =
1. Divide the coefficients 2. Subtract the exponents
cube root
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

30. What number multiplied by itself is equal to 16? The answer is 4. Why?
coefficient
Because 4 multiplied by itself equals 16.
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

31. To find the square root of any number - simply key in the number (the radicand) and press the
To multiply powers that have the same base:
change both terms in order to keep the value the same.
Calculator square-root key
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.

32. Any number with an exponent of 1 is equal to
2 x 10^9
itself
Same base
decrease the value of the exponent by 1 (dividing by 10)

33. To divide powers of ten:
10^-18
proper scientific
1. Divide the coefficients 2. Subtract the exponents
Because 4 multiplied by itself equals 16.

34. When the exponents are not the same
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
rewrite one of the terms so that the exponents are equal
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Because 4 multiplied by itself equals 16.

35. 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
radical sign
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
exponent

36.
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
move the decimal point the same number of units to the left
When moving the decimal point to the left (dividing by 10)

37. 1 to any power is equal to
1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
0
cubed

38. To multiply powers of 10:
itself
0
the radical sign with a little 3 that indicates the 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.

39. When you decrease the value of the power-of-10 exponent
0
one digit to the left of the decimal point
move the decimal point the same number of units to the right
exponent

40. 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
must be multiples of 3 or 0
change both terms in order to keep the value the same.
10^-2
move the decimal point the same number of units to the left

41. When you increase the value of the power-of-10 exponent
a fractional decimal
move the decimal point the same number of units to the left
the radical sign with a little 3 that indicates the cube root:
Same base

42. Any number with an exponent of 0 is equal to
Because 4 multiplied by itself equals 16.
Step 1. Divide the coefficients of the terms
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

43. Scientific notation requires there to be only
one digit to the left of the decimal point
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
squared
10^2

44. The square of 3 is
radical sign
base
proper scientific
9 (3^2 = 9)

45. 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.
perfect square
When the exponent of a power-of-10 expression is a negative integer:
Scientific notation
increase the power-of-10 exponent by the same number of units

46. 1 to any power is equal to
same exponent
decrease the value of the exponent by 1 (dividing by 10)
itself
1

47. Multiplying by 10
Moving the decimal point to the right
When the exponent of a power-of-10 expression is a negative integer:
decrease the value of the exponent by 1 (dividing by 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

48. 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.
Scientific notation
radical sign
Step 1. Divide the coefficients of the terms
move the decimal point the same number of units to the right

49. The cube root of zero is
Calculator square-root key
1
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
0

50. 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
increase the power-of-10 exponent by the same number of units
10^1
cubed