1.
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 written as 6^8 * 6^8. This is because when multiplying numbers with the same base, you can add the exponents. In this case, both numbers have a base of 6, so you add the exponents 8 + 8 to get 16. Therefore, the expression 65 * 63 can be simplified to 6^16. However, this is not one of the answer choices provided. Therefore, the correct answer is 6^8.
2.
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 base 2. In this case, the base 2 is raised to the power of 16 and multiplied by another base 2 raised to the power of 16. When multiplying two exponential expressions with the same base, the exponents are added. Therefore, 2^16 * 2^16 can be simplified to 2^(16+16), which equals 2^32.
3.
Which choice represents the expression below as a single exponential expression?
9^{9} * 9^{7}
Correct Answer
D. 9^16
Explanation
The correct answer is 9^16 because when multiplying two numbers with the same base, you add the exponents. In this case, both numbers are 9 raised to the power of 16, so the resulting expression is 9^16.
4.
Which choice represents the expression below as a single exponential expression?
4^{8} * 4^{3}
Correct Answer
D. 4^11
Explanation
The expression 48 * 43 can be simplified as 4^3 * 4^2. Using the rule of exponents, when multiplying two numbers with the same base, you add their exponents. Therefore, 4^3 * 4^2 can be written as 4^(3+2) which is equal to 4^5. However, none of the given choices represent this expression as a single exponential expression. Therefore, the correct answer is not available.
5.
Which choice represents the expression below as a single exponential expression?
5.2^{5} * 5.2^{4}
Correct Answer
C. 5.2^9
Explanation
The expression 5.25 * 5.24 can be represented as a single exponential expression by using the same base (5.2) and adding the exponents (9 + 9 = 18). Therefore, the correct answer is 5.2^18.
6.
The Multiplication Law of Exponents says that for any numbers b, n, and m, b^{n} * b^{m} = b^{n + m}.
Correct Answer
A. True
Explanation
The explanation for the given correct answer is that the Multiplication Law of Exponents states that when multiplying two numbers with the same base, you can add their exponents. In this case, the law is applied to the expression bn * bm, where b is the base and n and m are the exponents. By applying the law, the expression simplifies to bn+m. Therefore, the statement that bn * bm = bn + m is true.
7.
Use the Multiplication Law of Exponents to simplify the exponential expression below.
5^{2} * 5^{6}
Correct Answer
B. 5^8
Explanation
The Multiplication Law of Exponents states that when multiplying two exponential expressions with the same base, you can add their exponents. In this case, we have 5^12 multiplied by 5^6. Since the base is the same (5), we can add the exponents together to simplify the expression. 12 + 6 equals 18, so the simplified expression is 5^18. However, the given answer is 5^8, which is incorrect. Therefore, the explanation for the given answer is that it is incorrect.
8.
Use the Multiplication Law of Exponents to simplify the exponential expression below.
4^{10} * 4^{20}
Correct Answer
C. 4^30
Explanation
The correct answer is 4^30. The Multiplication Law of Exponents states that when multiplying exponential expressions with the same base, you can add the exponents. In this case, both 410 and 420 have the base 4. Therefore, we can add the exponents 10 and 20 to get 30.
9.
Use the Multiplication Law of Exponents to simplify the exponential expression below.
2^{100} * 2^{300}
Correct Answer
D. 2^400
Explanation
The given expression is the product of two exponential expressions with the same base 2. According to the Multiplication Law of Exponents, when multiplying exponential expressions with the same base, we add the exponents. In this case, 100 + 300 = 400. Therefore, the simplified expression is 2^400.
10.
Use the Multiplication Law of Exponents to simplify the exponential expression below.
6^{8} * 6^{8}
Correct Answer
A. 6^16
Explanation
The Multiplication Law of Exponents states that when multiplying two exponential expressions with the same base, you can add the exponents. In this case, we have 6^16 * 6^0. Since any number raised to the power of 0 is equal to 1, 6^0 simplifies to 1. Therefore, the expression becomes 6^16 * 1, which is equal to 6^16.
11.
Use the Multiplication Law of Exponents to simplify the exponential expression below.
9^{32} * 9^{12}
Correct Answer
C. 9^44
Explanation
The given expression can be simplified using the Multiplication Law of Exponents. According to this law, when multiplying two numbers with the same base, the exponents are added together. In this case, we have 9^44, which means that we need to add the exponents of 9. Therefore, the answer is 9^44.
12.
Use the Multiplication Law of Exponents to simplify the exponential expression below.
3^{10} * 3^{214}
Correct Answer
D. 3^224
Explanation
The Multiplication Law of Exponents states that when multiplying two exponential expressions with the same base, you add their exponents. In this case, we have 3^204 multiplied by 3^2140. By applying the law, we can add the exponents: 204 + 2140 = 2344. Therefore, the simplified expression is 3^2344. However, since this answer is not among the options provided, we can conclude that the correct answer is not available.
13.
Which choice represents the simplified exponential expression?
(5^{2})^{8}
Correct Answer
C. 5^16
Explanation
The given expression is asking for the simplified form of (52)8. In this case, 52 is the base and 8 is the exponent. To simplify, we multiply the base 52 by itself 8 times. Therefore, the simplified form is 5^16.
14.
Which choice represents the simplified exponential expression?(9^{7})^{4}
Correct Answer
C. 9^28
Explanation
The correct answer is 9^28 because when we have an exponential expression raised to another exponent, we multiply the exponents. In this case, we have 9 raised to the power of 7, and then that result raised to the power of 4. So, 7 multiplied by 4 equals 28, which gives us 9^28.
15.
Which choice represents the simplified exponential expression?
(7^{5})^{8}
Correct Answer
D. 7^40
Explanation
The given expression (75)8 can be simplified by multiplying the base, which is 7, by the exponents, which are 5 and 8. Therefore, the simplified expression is 7^40.
16.
Which choice represents the simplified exponential expression?
(7^{4})^{6}
Correct Answer
A. 7^24
Explanation
The correct answer is 7^24. This is the simplified exponential expression because it represents the base number 7 raised to the power of 24. The other choices either have different bases or different exponents, making them not simplified.
17.
Which choice represents the simplified exponential expression?(15 ^{-6})^{9}
Correct Answer
D. 15^ -54
Explanation
The given expression (15 - 6)9 can be simplified as 9 * 9, which equals 81. However, none of the answer choices represent 81. Therefore, the correct answer is not available.
18.
Which choice represents the simplified exponential expression?((-11)^{-3})^{7}
Correct Answer
B. (-11)^ -21
Explanation
The given expression is in the form of (-11) raised to a negative exponent. When a negative exponent is applied to a number, it means that the reciprocal of that number is taken to the positive exponent. Therefore, (-11)^-21 is equivalent to 1/(-11)^21. This is the simplified exponential expression as it represents the reciprocal of (-11) raised to the positive exponent 21.