Power Rule of Exponents Quick Check
Math 8 Q1 (Pre-Algebra) / Exponent Rules
Which expression is correctly developed to use the Power Rule of Exponents?(1 point)
Responses
(7^8)⋅(7^10)
left parenthesis 7 superscript 8 baseline right parenthesis times left parenthesis 7 superscript 10 baseline right parenthesis
(7^4)^8
left parenthesis 7 superscript 4 baseline right parenthesis superscript 8 baseline
12^9
12 superscript 9 baseline
(−5)^0
Which of the following correctly used the Power Rule of Exponents in the expression (10^9)^7?(1 point)
Responses
10^2
10 superscript 2 baseline
10^63
10 superscript 63 baseline
90^7
10^16
If the expression 4^10 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression? (1 point)
Responses
(4^12)^2
left parenthesis 4 superscript 12 baseline right parenthesis squared
(4^2)^8
left parenthesis 4 squared right parenthesis superscript 8 baseline
(4^5)^2
left parenthesis 4 superscript 5 baseline right parenthesis squared
4⋅4⋅4⋅4⋅4⋅4⋅4
Use the Power Rule of Exponents to create an expression equivalent to (156)2.(1 point)
Responses
15^8
15 superscript 8 baseline
15^4
15 superscript 4 baseline
15^12
15 superscript 12 baseline
15^3
15 cubed
What exponent would make the two expressions equivalent: (3^3)^x = 3^24?(1 point)
Responses
15
21
8
27
what is the correct answer to all 5 of the questions
1) (7^8)⋅(7^10)
2) 10^63
3) 4^10: (4^5)^2
4) (156)^2: 15^4
5) (3^3)^x = 3^24: x = 8
To determine the correct answer for each of the questions, let's review the Power Rule of Exponents:
Power Rule: For any base "a" and exponents "m" and "n", (a^m)^n = a^(m*n).
Now, let's go through each question and apply the Power Rule of Exponents to find the correct answer.
1. Which expression is correctly developed to use the Power Rule of Exponents?
The correct expression is (7^8)⋅(7^10). This follows the Power Rule: (a^m) * (a^n) = a^(m + n). Therefore, (7^8) * (7^10) = 7^(8 + 10) = 7^18.
2. Which of the following correctly used the Power Rule of Exponents in the expression (10^9)^7?
The correct choice is 10^63. Applying the Power Rule, (10^9)^7 = 10^(9*7) = 10^63.
3. If the expression 4^10 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression?
The correct expression is 4⋅4⋅4⋅4⋅4⋅4⋅4. The Power Rule is not used here because the exponents are already multiplied. So 4^10 simply means multiplying 4 by itself 10 times.
4. Use the Power Rule of Exponents to create an expression equivalent to (156)^2.
The correct expression is 156^2. Applying the Power Rule, (156)^2 = 156^(2*1) = 156^2.
5. What exponent would make the two expressions equivalent: (3^3)^x = 3^24?
To make the two expressions equivalent, we need to set the exponents equal to each other. Therefore, 3^(3*x) = 3^24. From this, we can conclude that 3x = 24. Solving for x, we find that x = 8.
So the correct answers are:
1. (7^8)⋅(7^10)
2. 10^63
3. 4⋅4⋅4⋅4⋅4⋅4⋅4
4. 156^2
5. 8
The correct answers for the questions are as follows:
1. (7^8)⋅(7^10)
This expression correctly uses the Power Rule of Exponents.
2. (10^63)
This expression correctly uses the Power Rule of Exponents in the expression (10^9)^7.
3. (4^12)^2
This is an equivalent expanded expression of 4^10 using the Power Rule of Exponents.
4. 15^4
This expression is equivalent to (156)2 using the Power Rule of Exponents.
5. 8
The exponent that would make the two expressions equivalent: (3^3)^x = 3^24, is 8.