1.
Correct Answer
C.
Explanation
Quotient Rule and Negative Exponent Rule
2.
Correct Answer
B.
Explanation
Power rule of exponents
3.
Correct Answer
A.
Explanation
Product Rule
4.
Write the number is scientific notation
0.00098
Correct Answer
C. 9.8 x 10 ^ -4
Explanation
The given number, 0.00098, can be written in scientific notation as 9.8 x 10^-4. This is because when we move the decimal point 4 places to the right, we get 9.8. The negative exponent of -4 indicates that the decimal point has been moved to the left, making the number smaller.
5.
Write the number is scientific notation
1,420,000
Correct Answer
A. 1.42 x 10 ^ 6
Explanation
The number 1,420,000 can be expressed in scientific notation as 1.42 x 10^6. In scientific notation, the number is written as a decimal between 1 and 10 (in this case, 1.42) multiplied by a power of 10 (in this case, 10^6). This notation is used to represent very large or very small numbers in a more concise and standardized format.
6.
Write the number is standard form
5.34 x 10 ^ -4
Correct Answer
B. 0.000534
Explanation
The given number, 5.34 x 10^-4, is written in scientific notation. In standard form, we move the decimal point 4 places to the left because the exponent is negative. Therefore, the correct answer is 0.000534.
7.
3.2501 x 10 ^ 7
Correct Answer
A. 32,501,000
Explanation
The correct answer is 32,501,000 because it is the only option that matches the given number, 3.2501 x 10^7, when written in standard form. The other options either have additional decimal places or do not have the correct number of digits.
8.
Correct Answer
C.
Explanation
Negative Exponent Rule
9.
Correct Answer
C. 1
Explanation
Zero Exponent Rule
10.
Correct Answer
B. 9
Explanation
Quotient Rule for Exponents
11.
Correct Answer
B. -36
12.
Correct Answer
A. True
Explanation
Product Rule for Exponents
13.
Correct Answer
C. 8
14.
Which choice represents the expression below as a single exponential expression?
9^{9} * 9^{7}
Correct Answer
D. 9^16
Explanation
The expression 99 * 97 can be written as 9^2 * 9^16. When multiplying two numbers with the same base, the exponents can be added together. Therefore, 9^2 * 9^16 simplifies to 9^18. However, none of the answer choices represent 9^18. The closest answer choice is 9^16, which is the correct answer.
15.
Which choice represents the expression below as a single exponential expression?
2^{11} * 2^{5}
Correct Answer
B. 2^16
Explanation
The given expression can be represented as a single exponential expression by adding the exponents of the same base. In this case, the base is 2 and the exponents are 16 and 16. When we add these exponents, we get 32. Therefore, the expression 2^16 * 2^16 can be simplified to 2^32.
16.
Which choice represents the expression below as a single exponential expression?
6^{5} * 6^{3}
Correct Answer
D. 6^8
Explanation
The expression 65 * 63 can be represented as 6^8 since both numbers can be expressed as powers of 6.
17.
Which choice represents the expression below as a single exponential expression?
4^{8} * 4^{3}
Correct Answer
D. 4^11
18.
Which choice represents the simplified exponential expression?
(5^{2})^{8}
Correct Answer
C. 5^16
Explanation
The correct answer is 5^16 because it represents the simplified exponential expression. The base, which is 5, is raised to the power of 16, resulting in a single term with no other operations or simplifications possible.
19.
Which choice represents the simplified exponential expression?
(9^{7})^{4}
Correct Answer
C. 9^28
Explanation
The correct answer is 9^28. This is the simplified exponential expression because it represents the base number 9 raised to the power of 28.
20.
Which choice represents the simplified exponential expression?
(7^{5})^{8}
Correct Answer
D. 7^40
Explanation
The correct answer is 7^40 because it represents the simplified exponential expression. The expression 7^40 means multiplying 7 by itself 40 times, resulting in a very large number.
21.
Which choice represents the simplified exponential expression?
(7^{4})^{6}
Correct Answer
A. 7^24
Explanation
The given expression is 7^24, which represents the simplified exponential expression. This is because 7^24 means multiplying 7 by itself 24 times, resulting in a very large number. Therefore, the correct answer is 7^24.
22.
Which choice represents the simplified exponential expression?
(15 ^{-6})^{9}
Correct Answer
D. 15^ -54
Explanation
The given expression can be simplified by multiplying the terms inside the parentheses, which results in (9)9. This further simplifies to 81. However, none of the answer choices represent this simplified exponential expression, so the correct answer is not available.
23.
Which choice represents the simplified exponential expression?
((-11)^{-3})^{7}
Correct Answer
B. (-11)^ -21
Explanation
The correct answer is (-11)^ -21. This is the simplified exponential expression because it represents raising -11 to the power of -21. The negative exponent indicates that the base (-11) should be inverted, and the positive exponent indicates how many times it should be multiplied. Therefore, (-11)^ -21 represents dividing 1 by (-11) 21 times.
24.
If the answer is 5 what is the cube root ?
Correct Answer
C. 125
Explanation
The cube root of 125 is 5 because when you multiply 5 by itself three times (5 x 5 x 5), you get 125. The cube root is the number that, when multiplied by itself three times, gives the original number. Therefore, 5 is the cube root of 125.
25.
The cube root of 216 is 6. true or false?
Correct Answer
A. True
Explanation
The cube root of a number is a value that, when multiplied by itself three times, gives the original number. In this case, if we multiply 6 by itself three times (6 x 6 x 6), we get 216. Therefore, the statement that the cube root of 216 is 6 is true.
26.
If the volume of a cube is 64 inches. What is the length of edges?
Correct Answer
B. 4
Explanation
The volume of a cube is calculated by multiplying the length of its edges three times. In this case, the volume is given as 64 inches, so we need to find the length of the edges. By taking the cube root of 64, we get 4. Therefore, the length of the edges of the cube is 4 inches.
27.
If the volume of a cube is 512 feet. What is the length of its edges?
Correct Answer
A. 8 feet
Explanation
The volume of a cube is calculated by multiplying the length of one of its edges by itself three times. In this case, the volume is given as 512 feet. To find the length of the edges, we need to find the cube root of the volume. The cube root of 512 is 8, so the length of each edge of the cube is 8 feet.
28.
The E coli bacterium is about 5 x 10^-7 meters wide. A hair is about 1.7 x 10^-5 meters wide. Whick is wider, the bacterium or the hair?
Correct Answer
B. Hair
Explanation
The hair is wider than the E. coli bacterium. The given measurements indicate that the hair is approximately 34 times wider than the bacterium.
29.
Correct Answer
B. 4 x 10^1 = 40
Explanation
Division: Subtract the exponents: (-2) - (-3) = +1
30.
Is the following numbers in proper scientific notation? 23.2 x 10^{2}
Correct Answer
B. No, this is not proper scientific notation
Explanation
2.32 x 10^3
31.
Do NOT use your calculator. UNDERSTAND how to work with scientific notation!
(10^{12 }is the same as 10^12)
(3.0x 10^{7})^{ }(4.0 x 10^{5}) =
Correct Answer
C. 1.2 x 10^13
Explanation
When MULTIPLYING in scientific notation, ADD the exponent.
Make sure you change your answer to proper scientific notation. (3.0x 10^7) (4.0 x 10^5)= (3.0 x 4.0)x 10^(7+5)
32.
Correct Answer
C. 3.0 x 10^1
Explanation
Dividing scientific notation: SUBTRACT the exponenent in the numerator from the exponent in the demoninator:
9.0 x 10^3 divided by 3.0 x 10^2 =
(9 divided by 3)x 10^(3-2)
33.
(8.0 x 10^{-2}) x (3 x 10^{-3}) =
Correct Answer
D. 2.4 x 10^-4
Explanation
When multiplying with scientific notation: add the exponents.
(8.0 x 10^-2) x (3 x 10^-3) = (8 x 3)x 10^(-2 + -3) = 24 x 10^-5 = 2.4 x 10^-4
34.
Which list has the numbers in order from least to greatest?
Correct Answer
B. 5.4 × 10^3, 4.5 × 10^4, 5.4 × 10^4
Explanation
The correct answer is 5.4 × 10^3, 4.5 × 10^4, 5.4 × 10^4. The numbers are arranged in order from least to greatest by comparing the coefficients (5.4 and 4.5) first. Since 4.5 is smaller than 5.4, it comes before 5.4 in the list. Then, we compare the exponents (10^3 and 10^4). 10^3 is smaller than 10^4, so it comes before 10^4 in the list. Therefore, the correct order is 5.4 × 10^3, 4.5 × 10^4, 5.4 × 10^4.