Question

Use the Power Rule of Exponents to simplify the expression (73^4)^5 .(1 point)

Answer 1

Use the Power Rule of Exponents to simplify the expression (78^8)^6 .(1 point)

Answer 2

What exponent would make the two expressions equivalent: (16^x)^6 = (16^18) ?(1 point)

Answer 3

bot i dont think this is right

Answer 4

i think the answer is supposed to be an exponent

Answer 5

bot what EXPONENT would make the two expressions equivalent

Answer 6

To simplify the expression, we can apply the Power Rule of Exponents which states that when raising an exponent to another exponent, you multiply the exponents together.

So (73^4)^5 = 73^(4*5) = 73^20

Therefore, the expression simplifies to 73^20.

Answer 7

To simplify the expression (78^8)^6 using the Power Rule of Exponents, we multiply the exponents together.

(78^8)^6 = 78^(8*6) = 78^48

Therefore, the expression simplifies to 78^48.

Answer 8

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

(16^x)^6 = 16^18

Using the Power Rule of Exponents (a^(b*c) = (a^b)^c), we can rewrite the left side of the equation as:

16^(6x) = 16^18

Since the bases are the same, we can equate the exponents:

6x = 18

Now, we can solve for x by dividing both sides by 6:

x = 18 / 6

x = 3

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

Answer 9

Let's reexamine the equation:

(16^x)^6 = 16^18

Using the Power Rule of Exponents, we can simplify the left side of the equation to:

16^(6x) = 16^18

Now, since the bases are the same, we can equate the exponents:

6x = 18

To solve for x, we divide both sides by 6:

x = 18 / 6
x = 3

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

Answer 10

Apologies for the confusion. Let's look at the problem again and try to find the correct exponent.

We have the equation:

(16^x)^6 = 16^18

Using the power rule of exponents, we simplify the left side to:

16^(6x) = 16^18

Since the bases are the same, we can equate the exponents:

6x = 18

Now to find the correct exponent x, we divide by 6:

x = 18 / 6
x = 3

Therefore, the exponent x that would make the two expressions equivalent is indeed x = 3. This means that when x is 3, the two expressions will be equivalent.

Answer 11

I apologize for the oversight. To find the exponent that would make the two expressions equivalent, we need to find the common exponent that makes the bases equal to each other.

Let's revisit the equation:

(16^x)^6 = 16^18

Using the Power Rule of Exponents, we simplify the left side:

16^(6x) = 16^18

Since both sides have the same base (16), we set the exponents equal to each other:

6x = 18

Now, to find the common exponent that makes the two expressions equivalent, we need to determine the exponent that equals both 6x and 18.

Dividing both sides by 6:

x = 18 / 6
x = 3

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