Apply the Quotient Rule of Integer Exponents to simplify 2365÷2332
97
23^97
23^33
1^33
To simplify 2365÷2332 using the Quotient Rule of Integer Exponents, we subtract the exponents when dividing with the same base. In this case, the base is 23.
Using the Quotient Rule, we have:
23^(2365-2332)
This simplifies to:
23^33
can you explain
Certainly!
The Quotient Rule of Integer Exponents states that when dividing two numbers with the same base, we subtract the exponents. In this case, we have the expression 2365÷2332.
Since both numbers have the same base of 23, we can apply the Quotient Rule. The exponent of 2365 is 2365, and the exponent of 2332 is 2332.
So, applying the Quotient Rule, we subtract the exponents:
23^(2365-2332)
This simplifies to:
23^33
Therefore, the simplified expression is 23^33.
To simplify the expression 2365 ÷ 2332 using the Quotient Rule of Integer Exponents, we need to subtract the exponents.
Let's break down the steps:
Step 1: Subtract the exponents.
The Quotient Rule states that when you divide two numbers with the same base, you need to subtract the exponents.
So, 2365 ÷ 2332 can be simplified as 23^(65-32).
Step 2: Simplify the exponent.
65 - 32 = 33
Therefore, 2365 ÷ 2332 simplifies to 23^33.
So, the simplified expression is 23^33.
To apply the Quotient Rule of Integer Exponents, we need to have the same base for both numbers being divided. In this case, we have 2365 divided by 2332, both of which are not in the form of a base raised to an exponent.
However, if we break down 2365 and 2332 into their prime factors, we can simplify the expression:
Prime factorization of 2365: 2365 = 5 * 7 * 13 * 23
Prime factorization of 2332: 2332 = 2 * 2 * 7 * 7 * 7
Now, let's cancel out the common factors:
2365 ÷ 2332
= (5 * 7 * 13 * 23) ÷ (2 * 2 * 7 * 7 * 7)
= (5 * 13 * 23) ÷ (2 * 2 * 7 * 7 * 7)
Notice that all the factors that remain on the numerator and denominator are prime numbers.
Therefore, the simplified expression is (5 * 13 * 23) ÷ (2 * 2 * 7 * 7 * 7).
So, the answer is not one of the given options.