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CLEP General Mathematics: Powers Exponents And Roots

Subjects : clep, math

Instructions:

Answer 50 questions in 20 minutes. 1 minute extra for reading the instructions.
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. What number multiplied by itself is equal to 16? The answer is 4. Why?
1
1
coefficient
Because 4 multiplied by itself equals 16.

2. Don't bother trying to find the square root of a negative number.
Subtract the exponent
The solution exists - but not in the real number system.
increase the power-of-10 exponent by the same number of units
cubed

3. The cube root of a negative number is also a
1
1
negative number
adjust the value of the coefficient

4. 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
decrease the power-of-10 exponent by the same number of units
base
adjust the value of the coefficient
1. Multiply the coefficients 2. Add the exponents

5. To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
1
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Engineering notation

6. Valid powers of 10 for engineering notation are:
base
you have to adjust the value of the exponent in order avoid changing the actual value.
0
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

7. To multiply powers of 10:
same 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.
Calculator square-root key
10^-18

8. Multiplying by 10
Moving the decimal point to the right
must be multiples of 3 or 0
1. Divide the coefficients 2. Subtract the exponents
adjust the value of the coefficient

9. When you move the decimal point in the coefficient to the right
same exponent
adjust the value of the coefficient
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
decrease the power-of-10 exponent by the same number of units

10. Any number with a negative exponent is equal to
6.74 x 10^-7
1
1 divided by that number with a positive exponent
cubed

11. 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
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
square root
1 divided by that number with a positive exponent

12. The cube root of zero is
cubed
0
cube-root key
decrease the value of the exponent by 1 (dividing by 10)

13. = 0.1 - or 1 with the decimal point moved one place to the left.
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
When the exponent of a power-of-10 expression is a negative integer:
Calculator square-root key
10^-1

14. 1 to any power is equal to
1. Divide the coefficients 2. Subtract the exponents
1
coefficient
Step 1. Divide the coefficients of the terms

15. Scientific notation requires there to be only
Scientific notation
perfect square
Same base
one digit to the left of the decimal point

16. When the exponents are not the same
rewrite one of the terms so that the exponents are equal
change both terms in order to keep the value the same.
0
radical sign

17. To multiply powers of ten:
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
0
1. Multiply the coefficients 2. Add the exponents
cube-root key

18. To multiply or divide exponent terms that do not have the same base:
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
2 x 10^9
10^2
10^-18

19. A number with an exponent of 2 is often said to be
1. Multiply the coefficients 2. Add the exponents
To multiply powers that have the same base:
0
squared

20. A very small number such as 0.000000674 can be written with scientific notation as
10^2
1
9 (3^2 = 9)
6.74 x 10^-7

21. A number with an exponent of 3 is often said to be
itself
0
cubed
base

22. 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
Scientific notation
the radical sign with a little 3 that indicates the cube root:
perfect square

23. To divide powers of ten:
0
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1. Divide the coefficients 2. Subtract the exponents
1

24. A number - when multiplied by itself - is equal to a given number.
1
1
1 divided by that number with a positive exponent
square root

25. 0^5 =
0
base
increase the power-of-10 exponent by the same number of units
proper scientific

26. 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.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
cube root
1
radical sign

27. To add or subtract numbers written with exponents:
square root
When the exponent of a power-of-10 expression is a negative integer:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
9 (3^2 = 9)

28. The square root of 9 is
3
When the exponent of a power-of-10 expression is a negative integer:
exponent
1

29. A negative exponent does not mean the decimal value is negative. It means the decimal value is
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
2 x 10^9
Engineering notation

30. 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.
increase the power-of-10 exponent by the same number of units
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:
5

31. Powers of ten can be added or subtracted only when their exponents
a fractional decimal
Are Equal
1
0

32. When you increase the value of the power-of-10 exponent
To multiply powers that have the same base:
move the decimal point the same number of units to the left
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
1

33. 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.
Same 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
Engineering notation
perfect square

34. 5^1 =
When the exponent of a power-of-10 expression is a negative integer:
5
Are Equal
Same base

35. 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.
10^-1
1
you have to adjust the value of the exponent in order avoid changing the actual value.

36. 1^4 =
1
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
Moving the decimal point to the right

37. Numbers with exponents can be directly multiplied or divided only when they have the
10^-18
0
Same base
itself

38. 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
Step 1. Divide the coefficients of the terms
Scientific notation
squared

39. Step 1: Add the exponents Step 2: Use the common base
Because 4 multiplied by itself equals 16.
squared
Same base
To multiply powers that have the same base:

40. 100 - or 1 with the decimal point moved two places to the right
10^2
2 x 10^9
squared
10^-18

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

42. 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
Moving the decimal point to the right
5
2
change both terms in order to keep the value the same.

43. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
0
base
2 x 10^9
exponent

44. 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 solution exists - but not in the real number system.
cube-root key
When the exponent of a power-of-10 expression is a negative integer:
3

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.
Same base
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
Engineering notation
cubed

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

47. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
radical sign
6.74 x 10^-7
10^-18

48. The symbol for the cube root of a number is
9 (3^2 = 9)
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
10^-1
the radical sign with a little 3 that indicates the cube root:

49. Represents 1 preceded by 17 zeros and a decimal point.
10^-18
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
rewrite one of the terms so that the exponents are equal
When moving the decimal point to the left (dividing by 10)

50. Indicates the number to be multiplied.
cubed
0
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
base