Asked by anonymous

use the product rule of exponents to simplify the expression 7^5*7^2

Answers

Answered by anonymous
hey bot,

find the numerical equivalent of 7^2*7^3
Answered by anonymous
hey bot,

find the numerical equivalent of 3^9*3^-5
Answered by anonymous
hey bot,

which expression is correctly developed to use the product rule of exponents?

a. 32^7

b. (5^2)^9

c. 6^2*7^3

d. 10^8*10*8
Answered by anonymous
will you check one more time to make sure?
Answered by anonymous
Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007?

a. 100^56

b. 200^15

c. 100^15

d. 10,000^15
Answered by anonymous
will you check one more time to make sure that is the correct answer?
Answered by anonymous
hey bot,

find the numerical equivalent of 10^2*10^3

a. 1,100

b. 100,000

c. 10^5

d.10
Answered by anonymous
will you double check to make sure that is the correct answer?
Answered by anonymous
find the numerical equivalent of 2^5*2^-2

a. 2

b. 16

c. 8

d. 128
Answered by GPT 3.5
To simplify the expression 7^5 * 7^2 using the product rule of exponents, we can add the exponents since the base (7) is the same:

7^5 * 7^2 = 7^(5 + 2).

Adding the exponents, we get:

7^(5 + 2) = 7^7.

Thus, the simplified expression is 7^7.
Answered by GPT 3.5
To find the numerical equivalent of 7^2 * 7^3, we can use the product rule of exponents again.

7^2 * 7^3 = 7^(2 + 3).

Adding the exponents, we get:

7^(2 + 3) = 7^5.

So, the numerical equivalent of 7^2 * 7^3 is 7^5, which evaluates to 16807.
Answered by GPT 3.5
To find the numerical equivalent of 3^9 * 3^-5, we can multiply the base (3) and add the exponents:

3^9 * 3^-5 = 3^(9 + (-5)).

Simplifying the exponent, we get:

3^(9 + (-5)) = 3^4.

Therefore, the numerical equivalent of 3^9 * 3^-5 is 3^4, which evaluates to 81.
Answered by GPT 3.5
The expression that is correctly developed to use the product rule of exponents is:

c. 6^2 * 7^3

The product rule of exponents states that when multiplying expressions with the same base, you can add the exponents. In this case, we have two different bases (6 and 7), so we cannot use the product rule of exponents to simplify their multiplication.
Answered by GPT 3.5
Apologies for the confusion. Let's double-check again.

The expression that is correctly developed to use the product rule of exponents is:

d. 10^8 * 10^8

In this case, both bases are the same (10), so we can use the product rule of exponents by adding the exponents:

10^8 * 10^8 = 10^(8 + 8) = 10^16

Therefore, the expression d. 10^8 * 10^8 is correctly developed to use the product rule of exponents.
Answered by GPT 3.5
To simplify the expression 1008 * 1007 using the product rule of exponents, we need to find an option where the exponent is the sum of the exponents of the base (in this case, 10).

Looking at the given options:

a. 100^56 does not have the same base as 1008 and 1007, so it is not using the product rule of exponents.

b. 200^15 does not have the same base as 1008 and 1007, so it is not using the product rule of exponents.

c. 100^15 is using the correct base (10) but has an exponent of 15, which is not the sum of the exponents of 1008 and 1007.

d. 10,000^15 is using the correct base (10) and the exponent is 15, which is the sum of the exponents of 1008 and 1007.

Therefore, the option that correctly uses the Product Rule of Exponents to simplify the expression 1008 * 1007 is d. 10,000^15.
Answered by GPT 3.5
Certainly, my apologies for any confusion. Let's review the options once again to ensure we have the correct answer.

To simplify the expression 1008 * 1007 using the product rule of exponents, we need to find an option that represents the same base (10) and has an exponent equal to the sum of the exponents.

Let's go through the options:

a. 100^56 - This option does not have the same base as 1008 and 1007, so it doesn't use the product rule of exponents.

b. 200^15 - This option also does not have the same base as 1008 and 1007, so it does not use the product rule of exponents.

c. 100^15 - Though this option has the same base of 10, the exponent 15 does not represent the sum of the exponents from 1008 and 1007.

d. 10,000^15 - This option has the same base (10) as 1008 and 1007, and the exponent (15) is indeed the sum of the exponents for 1008 and 1007.

Upon further review, it appears that option d. 10,000^15 is indeed the correct answer, as it correctly uses the product rule of exponents to simplify the expression 1008 * 1007.
Answered by GPT 3.5
To find the numerical equivalent of 10^2 * 10^3, we can use the product rule of exponents by adding the exponents since the base (10) is the same.

10^2 * 10^3 = 10^(2 + 3).

Adding the exponents, we get:

10^(2 + 3) = 10^5.

Therefore, the numerical equivalent of 10^2 * 10^3 is 10^5, which is option c. 10^5.
Answered by GPT 3.5
Apologies for any confusion caused. Let's double-check to ensure we have the correct answer.

To find the numerical equivalent of 10^2 * 10^3, we add the exponents:

10^2 * 10^3 = 10^(2 + 3).

Adding the exponents, we have:

10^(2 + 3) = 10^5.

Hence, the correct numerical equivalent of 10^2 * 10^3 is 10^5, which is option c. 10^5.

Therefore, after reaffirming, we can conclude that the answer is indeed option c. 10^5.

Related Questions