Question

Use the Power Rule of Exponents to simplify the expression (6^2)^4 .

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression (6^2)^4, we can use the Power Rule of Exponents. The rule states that when we raise a power to a power, we multiply the exponents.

In this case, the base is 6, and the first exponent is 2. So, we raise 6 to the power of 2:
6^2 = 36

Now, we take this result and raise it to the power of 4. This means we need to multiply the exponent 2 by 4:
36^4 = 36^(2 * 4) = 36^8

Therefore, the simplified expression is 36^8.

Answer 2

wrong

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake. Let's correct it.

To simplify the expression (6^2)^4, we can use the Power Rule of Exponents. The rule states that when we raise a power to another power, we multiply the exponents.

In this case, the base is 6^2, and the exponent is 4. So, we need to raise 6^2 to the power of 4.

6^2 = 36

Now, we raise 36 to the power of 4:
36^4 = (6^2)^4 = 6^(2 * 4) = 6^8

Therefore, the simplified expression is 6^8.

Answer 4

Use the Power Rule of Exponents to simplify the expression (73^4)^5 .

Answer 5

[AI-generated answer — Bot GPT 3.5]

To simplify the expression (73^4)^5, we can use the Power Rule of Exponents. The rule states that when we raise a power to a power, we multiply the exponents.

In this case, the base is 73^4, and the exponent is 5. So, we need to raise 73^4 to the power of 5.

To find 73^4, we raise 73 to the power of 4:
73^4 = 285,768,253

Now, we raise this result to the power of 5:
(73^4)^5 = (285,768,253)^5 = 2,042,225,353,675,895,582,394,413,929,301,189,560,516,209

Therefore, the simplified expression is 2,042,225,353,675,895,582,394,413,929,301,189,560,516,209.

Answer 6

simplify that

Answer 7

[AI-generated answer — Bot GPT 3.5]

Apologies for the incorrect response.

To simplify the expression (73^4)^5, we can use the power rule of exponents. The rule states that when we raise a power to a power, we multiply the exponents.

To simplify, we multiply the exponents:

4 * 5 = 20

Therefore, the simplified expression is 73^20.

Answer 8

Use the Power Rule of Exponents to simplify the expression (78^8)^6 .

Answer 9

[AI-generated answer — Bot GPT 3.5]

To simplify the expression (78^8)^6, we can use the Power Rule of Exponents, which states that when we raise a power to another power, we multiply the exponents.

In this case, the base is 78^8, and the exponent is 6. Therefore, we need to raise 78^8 to the power of 6.

To simplify, we multiply the exponents:

8 * 6 = 48

Thus, the simplified expression is 78^48.

Answer 10

Use the Power Rule of Exponents to create a simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12) .(1 point)

Answer 11

[AI-generated answer — Bot GPT 3.5]

To simplify the expression (12⋅12⋅12)⋅(12⋅12⋅12) using the Power Rule of Exponents, we can rewrite it as (12^3)⋅(12^3).

Now, using the Power Rule of Exponents, we can multiply the exponents:

3 + 3 = 6

Therefore, the simplified equivalent expression is 12^6.

Answer 12

What exponent would make the two expressions equivalent: (16^x)^6=(16^18) ?

Answer 13

[AI-generated answer — Bot GPT 3.5]

To find the exponent that would make the two expressions equivalent, we can set the exponents equal to each other and solve for x.

We have:

(16^x)^6 = 16^18

Applying the power rule of exponents, the exponent 6 can be distributed to both exponents inside the parentheses:

16^(6x) = 16^18

Since the bases are the same (16), we can equate the exponents:

6x = 18

Dividing both sides of the equation by 6, we get:

x = 3

Therefore, the exponent that would make the two expressions equivalent is x = 3.