Apply the quotient rule of integer exponents to simplify 2365÷2332

General
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apply the quotient rule of integer exponents to simplify 2365÷2332

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Apply the Quotient Rule of Integer Exponents to Simplify ( \frac{2365}{2332} )

Answer: To simplify the expression ( \frac{2365}{2332} ) using the quotient rule of integer exponents, let’s first understand what the quotient rule is. The quotient rule states that when you divide two exponential expressions that have the same base, you can subtract the exponent of the denominator from the exponent of the numerator. Mathematically, this is written as:

\frac{a^m}{a^n} = a^{m-n}

Now, let’s apply this rule to the expression you’ve provided:

  1. Identify the Base and Exponents:

    • The base here is 236 for both the numerator and the denominator.
    • The exponents are 5 and 2, respectively.

  2. Apply the Quotient Rule:

    • According to the quotient rule, we subtract the exponent in the denominator from the exponent in the numerator: ( 5 - 2 ).

  3. Simplify the Expression:

    • ( 236^{5-2} = 236^3 ).

Thus, the simplified form of the expression ( \frac{2365}{2332} ) is ( 236^3 ).

  1. Calculation (Optional for Understanding):
    • If you want to calculate ( 236^3 ), you would multiply 236 by itself three times:
      236 \times 236 \times 236 = 131,383,776.
    This exact calculation is often unnecessary unless you need a numerical answer rather than a simplified expression.

Summary of the Quotient Rule Application

By using the quotient rule, we’ve simplified the expression ( \frac{2365}{2332} ) to ( 236^3 ), effectively reducing the complexity of handling the numbers while maintaining their mathematical integrity. Remember, the key takeaway is that the quotient rule allows you to subtract the exponent of the divisor from the exponent of the dividend when the bases are identical. This simplifies complex divisions involving powers to more manageable calculations. If dealing with very large numbers, sometimes the simplified exponent form ((236^3)) is easier to work with symbolically.

@anonymous4