Apply the Quotient Rule of Integer Exponents to simplify 2365÷2332.(1 point)
Responses
97
97
1^33
1 superscript 33 baseline
23^97
23 superscript 97 baseline
2^333
2 superscript 333 baseline
To apply the Quotient Rule of Integer Exponents to simplify 2365÷2332, we can express both numbers in terms of their prime factorization and then cancel out the common factors.
Let's start by finding the prime factorization of 2365:
2365 = 5 * 7 * 67
Now let's find the prime factorization of 2332:
2332 = 2^2 * 7 * 83
Next, we can cancel out any common factors:
The common factor is 7.
So, 2365÷2332 simplifies to (5 * 67)÷(2^2 * 83).
This further simplifies to (5 * 67)÷4 * 83.
Therefore, the simplified expression is 335÷332.
To apply the Quotient Rule of Integer Exponents to simplify the expression 2365 ÷ 2332, we need to determine the base and the exponent for each number.
The first number, 2365, can be written as 2^3 * 5^1 * 11^1, where the exponents correspond to the prime factors of the number.
The second number, 2332, can be written as 2^2 * 7^1 * 83^1.
Now, using the Quotient Rule of Exponents, we subtract the exponents of common bases:
(2^3 * 5^1 * 11^1) ÷ (2^2 * 7^1 * 83^1) = 2^(3-2) * 5^(1-0) * 11^(1-0) * 7^0 * 83^0
Simplifying further, we get:
2^1 * 5^1 * 11^1 = 2 * 5 * 11 = 110
Therefore, when simplifying 2365 ÷ 2332 using the Quotient Rule of Integer Exponents, we get the result 110.