Apply the Quotient Rule of Integer Exponents to simplify 23^65 ÷ 23^32

Question

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options:

23^97

23^33

1^33

97

Answer 1

To simplify the expression \( 23^{65} \div 23^{32} \) using the Quotient Rule of Integer Exponents, we apply the rule which states that:

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

In this case, \( a = 23 \), \( m = 65 \), and \( n = 32 \). Thus, we have:

\[ 23^{65} \div 23^{32} = 23^{65 - 32} = 23^{33} \]

Therefore, the simplified expression is \( 23^{33} \).

The correct option is:

23^33