Simplify this expression using the Quotient Rule of Integer Exponents: 12^53 ÷ 7^53

Question

options:

5^106

5^53

12^106

12^53÷7^53

Answer 1

To simplify the expression \( 12^{53} \div 7^{53} \) using the Quotient Rule of Integer Exponents, we can rewrite it as:

\[ \frac{12^{53}}{7^{53}} = \left(\frac{12}{7}\right)^{53} \]

Thus, the simplified expression is \( \left(\frac{12}{7}\right)^{53} \).

Since this specific result is not one of the options provided (5^106, 5^53, 12^106, 12^53 ÷ 7^53), the closest match to express what we've done is \( 12^{53} ÷ 7^{53} \) itself, which is already in the form of the original expression.

So the choice that matches is:

12^53 ÷ 7^53.