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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. The square root of zero is
0
6.74 x 10^-7
cube root
exponent

2. Dividing by 10
Moving the decimal point to the left
1
base
increase the power-of-10 exponent by the same number of units

3. 1 to any power is equal to
10^-1
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1
move the decimal point the same number of units to the left

4. A number with an exponent of 3 is often said to be
1
base
Moving the decimal point to the left
cubed

5. To multiply powers of ten:
move the decimal point the same number of units to the right
1. Multiply the coefficients 2. Add the exponents
adjust the value of the coefficient
a fractional decimal

6. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
base
proper scientific
decrease the power-of-10 exponent by the same number of units
10^2

7. Multiplying by 10
0
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
10^-18

8. The square of 3 is
9 (3^2 = 9)
1
10^-18
must be multiples of 3 or 0

9. Don't bother trying to find the square root of a negative number.
Calculator square-root key
The solution exists - but not in the real number system.
0
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

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

11. The cube root of zero is
negative number
increase the power-of-10 exponent by the same number of units
5
0

12. 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
change both terms in order to keep the value the same.
0
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

13. 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
must be multiples of 3 or 0
5
base

14. Valid powers of 10 for engineering notation are:
10^-18
9 (3^2 = 9)
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
rewrite one of the terms so that the exponents are equal

15. To multiply powers of 10:
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. 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.
cube-root key

16. The decimal part
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
coefficient
Not

17. 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
same exponent
itself
must be multiples of 3 or 0
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

18. 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
cube-root key
Scientific notation
one digit to the left of the decimal point

19. 1 to any power is equal to
itself
move the decimal point the same number of units to the left
2 x 10^9
1

20. To add powers 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
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
2
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

21. 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
decrease the value of the exponent by 1 (dividing by 10)
change both terms in order to keep the value the same.
1

22. A number - when multiplied by itself - is equal to a given number.
one digit to the left of the decimal point
square root
0
Because 4 multiplied by itself equals 16.

23. The cube root of a negative number is also a
move the decimal point the same number of units to the left
negative number
0
1

24. Scientific notation requires there to be only
9 (3^2 = 9)
0
one digit to the left of the decimal point
adjust the value of the coefficient

25. 10 - or 1 with the decimal point moved one place to the right
1
10^1
perfect square
1 divided by that number with a positive exponent

26. A number is a second number which - when multiplied by itself three times - equals the original number.
decrease the power-of-10 exponent by the same number of units
cube-root key
cube root
adjust the value of the coefficient

27. 1^4 =
rewrite one of the terms so that the exponents are equal
the radical sign with a little 3 that indicates the cube root:
squared
1

28. When you change the position of the decimal point in a coefficient value
Calculator square-root key
squared
rewrite one of the terms so that the exponents are equal
you have to adjust the value of the exponent in order avoid changing the actual value.

29. 3^0 =
10^2
Step 1. Rewrite each number 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.
1

30. Powers of ten can be added or subtracted only when their exponents
10^2
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
9 (3^2 = 9)
Are Equal

31. To multiply or divide exponent terms that do not have the same base:
When the exponent of a power-of-10 expression is a negative integer:
1. Divide the coefficients 2. Subtract the exponents
you have to adjust the value of the exponent in order avoid changing the actual value.
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.

32. To divide powers that have the same base:
1
rewrite one of the terms so that the exponents are equal
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
9 (3^2 = 9)

33. Negative cube roots are okay ... negative square roots are
proper scientific
radical sign
Not
cube-root key

34. The symbol for the cube root of a number is
must be multiples of 3 or 0
5
Because 4 multiplied by itself equals 16.
the radical sign with a little 3 that indicates the cube root:

35. = 0.01 - or 1 with the decimal point moved two places to the left.
0
To multiply powers that have the same base:
10^-2
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

36. A number with an exponent of 2 is often said to be
exponent
decrease the power-of-10 exponent by the same number of units
squared
base

37. = 0.1 - or 1 with the decimal point moved one place to the left.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
radical sign
10^-1

38. Any number with a negative exponent is equal to
To multiply powers that have the same base:
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 right
1 divided by that number with a positive exponent

39. Valid powers-of-10 for engineering notation
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
must be multiples of 3 or 0
Are Equal

40. 0 to any power is equal to
0
one digit to the left of the decimal point
decrease the power-of-10 exponent by the same number of units
Are Equal

41. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
negative number
Step 1. Divide the coefficients of the terms
Subtract the exponent
itself

42. To divide powers of 10:
Are Equal
Step 1. Divide the coefficients of the terms
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
10^1

43. Any number with an exponent of 0 is equal to
proper scientific
perfect square
1
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

44. There are no special rules for adding and subtracting numbers that are written with exponents.
Moving the decimal point to the left
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
decrease 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.

45. 5^1 =
2
5
Scientific notation
the radical sign with a little 3 that indicates the cube root:

46. 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.
1
Moving the decimal point to the left
increase the power-of-10 exponent by the same number of units
radical sign

47. 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.
decrease the power-of-10 exponent by the same number of units
perfect square
cube root
1

48. The square root of 9 is
10^2
9 (3^2 = 9)
3
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten

49. 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.
Subtract the exponent
same exponent
10^-1
When the exponent of a power-of-10 expression is a negative integer:

50. When you move the decimal point in the coefficient to the right
Scientific notation
9 (3^2 = 9)
decrease the power-of-10 exponent by the same number of units
When the exponent of a power-of-10 expression is a negative integer: