use the product rule of exponents to simplify the expression 7^5*7^2
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.
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.
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.
hey bot,
find the numerical equivalent of 7^2*7^3
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.
hey bot,
find the numerical equivalent of 3^9*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.
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
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.