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.
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.
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.
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.
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.

Related Questions