Apply the Quotient Rule of Integer Exponents to simplify 2365÷2332
97
2397
23 superscript 97 baseline
2333
23 superscript 33 baseline
133
1 superscript 33 baseline
To simplify 2365 ÷ 2332, we can apply the quotient rule of integer exponents. According to the rule, when you divide two numbers with the same base raised to different exponents, you subtract the exponents.
In this case, we have 23³³ ÷ 23⁹⁷. By subtracting the exponents (33 - 97), we get 23^(33 - 97) = 23^(-64).
Therefore, 2365 ÷ 2332 simplifies to 23^(-64).
ok but which one
Apologies for the confusion. To clarify, the simplified expression for 2365 ÷ 2332 using the quotient rule of integer exponents is 23^(-64).
there is no 23^(-64)
Apologies for the error in the previous response. Let's simplify 2365 ÷ 2332 using the quotient rule of integer exponents correctly.
2365 ÷ 2332 can be written as (2^365) ÷ (2^332) since 2365 = 2^365 and 2332 = 2^332.
To divide two numbers with the same base raised to different exponents, we subtract the exponents. Therefore, (2^365) ÷ (2^332) simplifies to 2^(365 - 332) = 2^33.
Therefore, 2365 ÷ 2332 simplifies to 2^33.
To simplify the expression 2365÷2332 using the Quotient Rule of Integer Exponents, you can divide the exponents as follows:
The base number, 23, remains the same.
Then, subtract the exponent in the denominator from the exponent in the numerator:
65 - 32 = 33.
So, the simplified expression is 23^33.
To apply the Quotient Rule of Integer Exponents to simplify 2365 ÷ 2332, we need to subtract the exponents of the same base.
First, let's rewrite the numbers as powers of a common base, such as 23, where 23 is the base and the exponents represent the numbers:
2365 = 23^65
2332 = 23^32
Now, to divide the two numbers, we subtract the exponents:
23^65 ÷ 23^32 = 23^(65-32) = 23^33
So the simplified expression is 23^33.