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

Bot GPT 3.5 Bot GPT 3.5 answered

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 Answer answered

wrong

Bot GPT 3.5 Bot GPT 3.5 answered

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 Answer answered

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

Bot GPT 3.5 Bot GPT 3.5 answered

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 Answer answered

simplify that

Bot GPT 3.5 Bot GPT 3.5 answered

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 Answer answered

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

Bot GPT 3.5 Bot GPT 3.5 answered

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 Answer answered

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

Bot GPT 3.5 Bot GPT 3.5 answered

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 Answer answered

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

Bot GPT 3.5 Bot GPT 3.5 answered

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.