CLEP General Mathematics: Powers Exponents And Roots

Instructions:

• Answer 50 questions in 15 minutes.
• 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. A number with an exponent of 3 is often said to be
proper scientific
1
same exponent
cubed


2. When you decrease the value of the power-of-10 exponent
10^-1
move the decimal point the same number of units to the right
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
The solution exists - but not in the real number system.


3. When you move the decimal point in the coefficient to the left
exponent
When the exponent of a power-of-10 expression is a negative integer:
increase the power-of-10 exponent by the same number of units
1 divided by that number with a positive exponent


4. 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.
Subtract the exponent
perfect square
same exponent
0


5. Don't bother trying to find the square root of a negative number.
itself
squared
The solution exists - but not in the real number system.
cubed


6. 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
1
cube-root key
adjust the value of the coefficient
exponent


7. To find the square root of any number - simply key in the number (the radicand) and press the
the radical sign with a little 3 that indicates the cube root:
base
radical sign
Calculator square-root key


8. 1^4 =
1. Divide the coefficients 2. Subtract the exponents
1
Scientific notation
one digit to the left of the decimal point


9. Represents 1 preceded by 17 zeros and a decimal point.
10^-1
10^-18
decrease the value of the exponent by 1 (dividing by 10)
When the exponent of a power-of-10 expression is a negative integer:


10. When you change the position of the decimal point in a coefficient value
Are Equal
the radical sign with a little 3 that indicates the cube root:
2
you have to adjust the value of the exponent in order avoid changing the actual value.


11. Scientific notation requires there to be only
one digit to the left of the decimal point
same exponent
must be multiples of 3 or 0
proper scientific


12. When moving the decimal point to the right (multiplying by 10)
you have to adjust the value of the exponent in order avoid changing the actual value.
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
5
decrease the value of the exponent by 1 (dividing by 10)


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


14. = 0.1 - or 1 with the decimal point moved one place to the left.
cubed
1. Divide the coefficients 2. Subtract the exponents
10^-1
10^-2


15. The cube root of a negative number is also a
square root
negative number
1
itself


16. To multiply or divide exponent terms that do not have the same base:
Step 1. Divide the coefficients of the terms
9 (3^2 = 9)
adjust the value of the coefficient
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.


17. 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
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
change both terms in order to keep the value the same.
perfect square


18. A number is a second number which - when multiplied by itself three times - equals the original number.
cube root
5
proper scientific
Engineering notation


19. 10 - or 1 with the decimal point moved one place to the right
you have to adjust the value of the exponent in order avoid changing the actual value.
move the decimal point the same number of units to the left
a fractional decimal
10^1


20. 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.
0
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.
the radical sign with a little 3 that indicates the cube root:
radical sign


21. To multiply powers of 10:
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.
Because 4 multiplied by itself equals 16.
0
square root


22. To multiply powers of ten:
radical sign
When the exponent of a power-of-10 expression is a negative integer:
1. Multiply the coefficients 2. Add the exponents
coefficient


23. To divide powers of ten:
move the decimal point the same number of units to the right
Calculator square-root key
1. Divide the coefficients 2. Subtract the exponents
move the decimal point the same number of units to the left


24. To subtract powers of ten:
exponent
cubed
0
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten


25. A very small number such as 0.000000674 can be written with scientific notation as
1
6.74 x 10^-7
cube root
1. Divide the coefficients 2. Subtract the exponents


26. 0^5 =
exponent
cube-root key
0
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.


27. 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.
cubed
Engineering notation
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
square root


28. Any number with an exponent of 1 is equal to
itself
Subtract the exponent
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


29. Any number with an exponent of 0 is equal to
The solution exists - but not in the real number system.
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.
5
1


30. 5^1 =
the radical sign with a little 3 that indicates the cube root:
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
10^1
5


31. The square root of 9 is
3
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. Multiply the coefficients 2. Add the exponents


32. Valid powers of 10 for engineering notation are:
10^2
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
Because 4 multiplied by itself equals 16.
0


33. When this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
1
proper scientific
increase the power-of-10 exponent by the same number of units
Each number must first be converted to its ordinary decimal form - then complete the addition/subtraction operation.


34. Increase the value of the exponent by 1 (multiplying by 10)
0
When moving the decimal point to the left (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
cubed


35. To add or subtract numbers written with exponents:
1 divided by that number with a positive exponent
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
1. Divide the coefficients 2. Subtract the exponents
square root


36. The square of 3 is
9 (3^2 = 9)
change both terms in order to keep the value the same.
exponent
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0


37. To add powers of ten:
When the exponent of a power-of-10 expression is a negative integer:
1. Make sure the terms have the same power of ten. 2. Add the coefficients 3. Assign the common power of ten
The solution exists - but not in the real number system.
Moving the decimal point to the left


38. 3^0 =
1 divided by that number with a positive exponent
1
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0
a fractional decimal


39. The square root of zero is
Moving the decimal point to the left
0
The solution exists - but not in the real number system.
To multiply powers that have the same base:


40. 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
perfect square
To multiply powers that have the same base:
adjust the value of the coefficient
coefficient


41. A negative exponent does not mean the decimal value is negative. It means the decimal value is
perfect square
itself
2 x 10^9
a fractional decimal


42. 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
cube root
When moving the decimal point to the left (dividing by 10)
same exponent
10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0


43. When you move the decimal point in the coefficient to the right
increase the power-of-10 exponent by the same number of units
decrease the power-of-10 exponent by the same number of units
2
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.


44. 100 - or 1 with the decimal point moved two places to the right
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
Because 4 multiplied by itself equals 16.
10^2
1


45. Always 10 for scientific notation
proper scientific
1 divided by that number with a positive exponent
base
9 (3^2 = 9)


46. A very large number such as 2 -000 -000 -000 can be written with scientific notation as
1. Make sure the terms have the same power of ten. 2. Subtract the coefficients 3. Assign the common power of ten
1
2 x 10^9
squared


47. Powers of ten can be added or subtracted only when their exponents
you have to adjust the value of the exponent in order avoid changing the actual value.
Are Equal
10^1
one digit to the left of the decimal point


48. For the 10
exponent
Step 1. Divide the coefficients of the terms
square root
10^-1


49. 1 to any power is equal to
1
2 x 10^9
Subtract the exponent
move the decimal point the same number of units to the left


50. Numbers with exponents can be directly multiplied or divided only when they have the
base
2
Same base
10^2