To use the Power Rule of Exponents, we multiply the exponents for each situation.
1. (6^2)^4
= 6^(2*4)
= 6^8
2. (73^4)^5
= 73^(4*5)
= 73^20
3. (78^8)^6
= 78^(8*6)
= 78^48
4. (12⋅12⋅12)⋅(12⋅12⋅12)
= (12^3)⋅(12^3)
= 12^(3+3)
= 12^6
5. To make the two expressions equivalent, the exponent in the first expression must be x = 18/6 = 3.
Use the Power Rule of Exponents to simplify the expression (6^2)^4
Use the Power Rule of Exponents to simplify the expression (73^4)^5
Use the Power Rule of Exponents to simplify the expression (78^8)^6
Use the Power Rule of Exponents to create a simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12)
What exponent would make the two expressions equivalent: (16^x)^6=(16^18)?
17 answers
1. Which expression is correctly developed to use the Power Rule of Exponents?
12^9
(7^4)^8
(−5)^0
(7^8)⋅(7^10)
2.Which of the following correctly used the Power Rule of Exponents in the expression (10^9)^7?
10^16
10^63
10^2
90^7
3. If the expression 4^10 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression?
(4^12)^2
(4^2)^8
(4^5)^2
4 x 4 x 4 x 4 x 4 x 4 x 4
4. Use the Power Rule of Exponents to create and expression equivalent to (15^6)^2.
15^8
15^12
15^3
15^4
5. What exponent would make the two expressions equivalent: (3^3)^x = 3^24?
15
8
27
21
12^9
(7^4)^8
(−5)^0
(7^8)⋅(7^10)
2.Which of the following correctly used the Power Rule of Exponents in the expression (10^9)^7?
10^16
10^63
10^2
90^7
3. If the expression 4^10 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression?
(4^12)^2
(4^2)^8
(4^5)^2
4 x 4 x 4 x 4 x 4 x 4 x 4
4. Use the Power Rule of Exponents to create and expression equivalent to (15^6)^2.
15^8
15^12
15^3
15^4
5. What exponent would make the two expressions equivalent: (3^3)^x = 3^24?
15
8
27
21
1. (7^8)⋅(7^10) is correctly developed to use the Power Rule of Exponents because it combines the exponents when multiplying two powers with the same base.
2. 10^63 correctly uses the Power Rule of Exponents in the expression (10^9)^7. By multiplying the exponents, we get 9 x 7 = 63.
3. To find an equivalent expanded expression for 4^10 using the Power Rule of Exponents, we would first simplify the expression. However, none of the given options are correct. The correct equivalent expanded expression would be (4^10) or 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4.
4. To create an expression equivalent to (15^6)^2 using the Power Rule of Exponents, we need to multiply the exponents. Thus, the equivalent expression would be 15^(6*2) = 15^12.
5. The exponent that would make the two expressions (3^3)^x and 3^24 equivalent is 8. Since the base is the same in both expressions (3), we can set the exponents equal to each other: 3^3x = 3^24. By comparing the exponents, we see that 3x = 24, and solving for x, we get x = 8.
2. 10^63 correctly uses the Power Rule of Exponents in the expression (10^9)^7. By multiplying the exponents, we get 9 x 7 = 63.
3. To find an equivalent expanded expression for 4^10 using the Power Rule of Exponents, we would first simplify the expression. However, none of the given options are correct. The correct equivalent expanded expression would be (4^10) or 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4.
4. To create an expression equivalent to (15^6)^2 using the Power Rule of Exponents, we need to multiply the exponents. Thus, the equivalent expression would be 15^(6*2) = 15^12.
5. The exponent that would make the two expressions (3^3)^x and 3^24 equivalent is 8. Since the base is the same in both expressions (3), we can set the exponents equal to each other: 3^3x = 3^24. By comparing the exponents, we see that 3x = 24, and solving for x, we get x = 8.
The first one are the practice questions so that's 100%.
I'll let you know on the quickcheck next.
I'll let you know on the quickcheck next.
Thank you for letting me know! I apologize for the confusion earlier. If you have any more questions or need further assistance, please feel free to ask. Good luck with your quickcheck!
The quickcheck has 2 wrong. 1. is (7^4)^8 and 3. is (4^5)^2
I apologize for the incorrect answers in question 1 and question 3. Let's correct them:
1. (7^4)^8
Using the power rule of exponents, we multiply the exponents: 7^(4*8) = 7^32.
3. (4^5)^2
Similarly, we multiply the exponents: 4^(5*2) = 4^10.
I apologize for the confusion earlier. If you have any additional questions or need further clarification, please let me know.
1. (7^4)^8
Using the power rule of exponents, we multiply the exponents: 7^(4*8) = 7^32.
3. (4^5)^2
Similarly, we multiply the exponents: 4^(5*2) = 4^10.
I apologize for the confusion earlier. If you have any additional questions or need further clarification, please let me know.
Bot What exponent would make the two expressions equivalent: (3*3)*=3*24
It seems there might be a typo in your question. The expression (3*3)* does not have an exponent attached to it. However, if you meant to ask what exponent would make the two expressions equivalent: (3^3)^x = 3^24, I can help with that.
To find the value of x, we can set the exponents equal to each other:
(3^3)^x = 3^24
Using the power rule of exponents, we multiply the exponents on the left side:
3^(3x) = 3^24
Since the bases are the same, the exponents must be equal:
3x = 24
Dividing both sides by 3, we find:
x = 8
Therefore, the exponent that would make the two expressions equivalent is x = 8.
To find the value of x, we can set the exponents equal to each other:
(3^3)^x = 3^24
Using the power rule of exponents, we multiply the exponents on the left side:
3^(3x) = 3^24
Since the bases are the same, the exponents must be equal:
3x = 24
Dividing both sides by 3, we find:
x = 8
Therefore, the exponent that would make the two expressions equivalent is x = 8.
Use the Power Rule of Exponents to create an expression equivalent to (15*6)*2.
Sure! To create an equivalent expression using the Power Rule of Exponents, we can simplify the expression (15^6)^2.
Using the Power Rule of Exponents, we multiply the exponents:
(15^6)^2 = 15^(6*2) = 15^12.
Therefore, an equivalent expression to (15^6)^2 is 15^12.
Using the Power Rule of Exponents, we multiply the exponents:
(15^6)^2 = 15^(6*2) = 15^12.
Therefore, an equivalent expression to (15^6)^2 is 15^12.
If the expression 4*10 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression? (1 point)
If the expression 4*10 was simplified using the Power Rule of Exponents, we would not apply the Power Rule of Exponents because there are no exponents involved. The expression 4*10 is already simplified and cannot be further expanded using the Power Rule of Exponents.
Which of the following correctly used the Power Rule of Exponents in the expression (10*9)*7?
None of the given options correctly use the Power Rule of Exponents in the expression (10*9)*7.
The Power Rule of Exponents is used when we have a base raised to a power. In this expression, (10*9) is simply a multiplication, not an exponentiation. Therefore, the Power Rule of Exponents does not apply.
To evaluate (10*9)*7, we can simply perform the multiplication first:
(10*9)*7 = 90*7 = 630.
The Power Rule of Exponents is used when we have a base raised to a power. In this expression, (10*9) is simply a multiplication, not an exponentiation. Therefore, the Power Rule of Exponents does not apply.
To evaluate (10*9)*7, we can simply perform the multiplication first:
(10*9)*7 = 90*7 = 630.
wrong
Apologies for the confusion. Let's evaluate the expression (10*9)*7 using the Power Rule of Exponents.
The Power Rule of Exponents states that when you have a power raised to another power, you multiply the exponents. However, in this case, we don't have any exponents involved. The expression (10*9)*7 is simply a multiplication of numbers.
To simplify, we can perform the multiplication:
(10*9)*7 = 90*7 = 630.
Therefore, in this expression, the Power Rule of Exponents is not applicable.
The Power Rule of Exponents states that when you have a power raised to another power, you multiply the exponents. However, in this case, we don't have any exponents involved. The expression (10*9)*7 is simply a multiplication of numbers.
To simplify, we can perform the multiplication:
(10*9)*7 = 90*7 = 630.
Therefore, in this expression, the Power Rule of Exponents is not applicable.
3 answers