Question
Use the Power Rule of Exponents to simplify the expression (6 to the power of 2) to the power of 4
Answers
Answer
Use the Power Rule of Exponents to simplify the expression (73^4)^5
Answer
Use the Power Rule of Exponents to simplify the expression (78^8)^6
Answer
Use the Power Rule of Exponents to create a simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12)
Answer
What exponent would make the two expressions equivalent: (16^x)^6 = (16^18)
Answered by
GPT 3.5
To simplify the expression (6^2)^4 using the Power Rule of Exponents, we need to multiply the exponents.
First, simplify the exponent of 6^2- which is 2 since it's raised to the power of 4.
So we have (6^2)^4 = 6^(2*4).
Then, calculate the exponent 2 * 4 which is equal to 8.
Thus, (6^2)^4 simplifies to 6^8.
First, simplify the exponent of 6^2- which is 2 since it's raised to the power of 4.
So we have (6^2)^4 = 6^(2*4).
Then, calculate the exponent 2 * 4 which is equal to 8.
Thus, (6^2)^4 simplifies to 6^8.
Answered by
GPT 3.5
To simplify the expression (73^4)^5 using the Power Rule of Exponents, we will multiply the exponents.
First, we simplify the exponent of 73^4, which is 4 since it is raised to the power of 5.
So we have (73^4)^5 = 73^(4*5).
Then, we calculate the exponent 4 * 5, which is equal to 20.
Thus, (73^4)^5 simplifies to 73^20.
First, we simplify the exponent of 73^4, which is 4 since it is raised to the power of 5.
So we have (73^4)^5 = 73^(4*5).
Then, we calculate the exponent 4 * 5, which is equal to 20.
Thus, (73^4)^5 simplifies to 73^20.
Answered by
GPT 3.5
To simplify the expression (78^8)^6 using the Power Rule of Exponents, we will multiply the exponents.
First, we simplify the exponent of 78^8, which is 8 since it is raised to the power of 6.
So we have (78^8)^6 = 78^(8*6).
Then, we calculate the exponent 8 * 6, which is equal to 48.
Thus, (78^8)^6 simplifies to 78^48.
First, we simplify the exponent of 78^8, which is 8 since it is raised to the power of 6.
So we have (78^8)^6 = 78^(8*6).
Then, we calculate the exponent 8 * 6, which is equal to 48.
Thus, (78^8)^6 simplifies to 78^48.
Answered by
GPT 3.5
Using the Power Rule of Exponents, we can rewrite the expression (12⋅12⋅12)⋅(12⋅12⋅12) as (12^3)⋅(12^3).
Now, we can apply the Power Rule of Exponents, which states that when multiplying two powers with the same base, we can add their exponents.
So, (12^3)⋅(12^3) can be simplified as 12^(3+3), which is equal to 12^6.
Therefore, the simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12) is 12^6.
Now, we can apply the Power Rule of Exponents, which states that when multiplying two powers with the same base, we can add their exponents.
So, (12^3)⋅(12^3) can be simplified as 12^(3+3), which is equal to 12^6.
Therefore, the simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12) is 12^6.
Answered by
GPT 3.5
To find the exponent that would make the two expressions equivalent, we can equate the exponents of the base 16.
We have (16^x)^6 = (16^18).
According to the Power Rule of Exponents, when raising a power to another power, we need to multiply the exponents. Therefore, we can simplify the left side of the equation as 16^(6x).
Now, we can equate the exponents:
6x = 18.
To solve for x, we divide both sides of the equation by 6:
x = 18/6.
Simplifying further, we get:
x = 3.
Therefore, the exponent that would make the two expressions equivalent is x = 3.
We have (16^x)^6 = (16^18).
According to the Power Rule of Exponents, when raising a power to another power, we need to multiply the exponents. Therefore, we can simplify the left side of the equation as 16^(6x).
Now, we can equate the exponents:
6x = 18.
To solve for x, we divide both sides of the equation by 6:
x = 18/6.
Simplifying further, we get:
x = 3.
Therefore, the exponent that would make the two expressions equivalent is x = 3.
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