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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. Always 10 for scientific notation
Not
squared
base
exponent

2. The decimal part
coefficient
10^-2
change both terms in order to keep the value the same.
decrease the value of the exponent by 1 (dividing by 10)

3. 1^4 =
same exponent
2
1
cubed

4. What number multiplied by itself is equal to 16? The answer is 4. Why?
cube-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.
cubed
Because 4 multiplied by itself equals 16.

5. 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
squared
Moving the decimal point to the right
Scientific notation

6. 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.
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Engineering notation
When the exponent of a power-of-10 expression is a negative integer:
move the decimal point the same number of units to the left

7. 0^5 =
10^-1
1. Multiply the coefficients 2. Add the exponents
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
0

8. 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.
Scientific notation
rewrite one of the terms so that the exponents are equal
0

9. When you move the decimal point in the coefficient to the left
increase the power-of-10 exponent by the same number of units
0
1. Make sure the terms have the same power of ten. 2. Add 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

10. Numbers with exponents can be directly multiplied or divided only when they have the
Step 1. Divide the coefficients of the terms
1
Same base
you have to adjust the value of the exponent in order avoid changing the actual value.

11. The square root of 9 is
3
0
The solution exists - but not in the real number system.
10^-18

12. = 0.01 - or 1 with the decimal point moved two places to the left.
10^-2
increase the power-of-10 exponent by the same number of units
same exponent
3

13. 5^1 =
5
10^1
radical sign
square root

14. A number is a second number which - when multiplied by itself three times - equals the original number.
Same base
cube root
To multiply powers that have the same base:
cube-root key

15. A negative exponent does not mean the decimal value is negative. It means the decimal value is
same exponent
exponent
a fractional decimal
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten

16. Any number with an exponent of 0 is equal to
Because 4 multiplied by itself equals 16.
1
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)

17. What number multiplied by itself is equal to 4? Well - 2. x 2 = 4 - so the answer is
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
2
Moving the decimal point to the left
1

18. To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
1 divided by that number with a positive exponent
perfect square
Subtract the exponent
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

19. 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
1
cube root
square root

20. To add or subtract numbers written with exponents:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
Scientific notation
one digit to the left of the decimal point
1

21. To add 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
decrease the power-of-10 exponent by the same number of units
1 divided by that number with a positive exponent
exponent

22. When you move the decimal point in the coefficient to the right
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
The solution exists - but not in the real number system.
1
decrease the power-of-10 exponent by the same number of units

23. Negative cube roots are okay ... negative square roots are
To multiply powers that have the same base:
9 (3^2 = 9)
10^2
Not

24.
1
10^-18
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

25. 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
5
you have to adjust the value of the exponent in order avoid changing the actual value.
cube-root key
rewrite one of the terms so that the exponents are equal

26. Step 1: Add the exponents Step 2: Use the common base
To multiply powers that have the same base:
1
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

27. When moving the decimal point to the right (multiplying by 10)
Are Equal
Moving the decimal point to the left
0
decrease the value of the exponent by 1 (dividing by 10)

28. 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
0
perfect square
cube-root key
same exponent

29. 10 - or 1 with the decimal point moved one place to the right
10^1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
squared
5

30. = 0.1 - or 1 with the decimal point moved one place to the left.
a fractional decimal
10^-1
decrease the value of the exponent by 1 (dividing by 10)
9 (3^2 = 9)

31. 1 to any power is equal to
5
1
Same base
increase the power-of-10 exponent by the same number of units

32. A number with an exponent of 2 is often said to be
0
1
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.
squared

33. 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.
5
radical sign
Not
1. Multiply the coefficients 2. Add the exponents

34. Any number with an exponent of 1 is equal to
decrease the value of the exponent by 1 (dividing by 10)
itself
cube-root key
0

35. When you change the position of the decimal point in a coefficient value
6.74 x 10^-7
you have to adjust the value of the exponent in order avoid changing the actual value.
Not
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.

36. Valid powers of 10 for engineering notation are:
exponent
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
exponent
The solution exists - but not in the real number system.

37. Powers of ten can be added or subtracted only when their exponents
Are Equal
square root
Step 1. Divide the coefficients of the terms
radical sign

38. 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
Not
2 x 10^9
itself

39. When the exponents are not the same
5
rewrite one of the terms so that the exponents are equal
9 (3^2 = 9)
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

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
negative number
6.74 x 10^-7
change both terms in order to keep the value the same.
1

41. Indicates the number of times the base is to be multiplied.
decrease the power-of-10 exponent by the same number of units
Same base
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
exponent

42. To multiply powers of ten:
1. Multiply the coefficients 2. Add the exponents
Subtract the exponent
Are Equal
2 x 10^9

43. When you decrease the value of the power-of-10 exponent
Are Equal
0
move the decimal point the same number of units to the right
must be multiples of 3 or 0

44. A very small number such as 0.000000674 can be written with scientific notation as
1
6.74 x 10^-7
Step 1. Divide the coefficients of the terms
move the decimal point the same number of units to the left

45. 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.
Engineering notation
base
1
1. Multiply the coefficients 2. Add the exponents

46. To divide powers of ten:
When moving the decimal point to the left (dividing by 10)
radical sign
Calculator square-root key
1. Divide the coefficients 2. Subtract the exponents

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.
perfect square
When the exponent of a power-of-10 expression is a negative integer:
5
Subtract the exponent

48. Represents 1 preceded by 17 zeros and a decimal point.
itself
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^-18
decrease the power-of-10 exponent by the same number of units

49. 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
1. Multiply the coefficients 2. Add the exponents
10^-2
adjust the value of the coefficient
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base

50. The cube root of zero is
0
3
The solution exists - but not in the real number system.
10^-2