The Quotient of Powers in Mathematics

What is the concept of the Quotient of Powers?

The expression 3^10 / 3^4 belongs to which property in mathematics?

The concept of the Quotient of Powers in mathematics deals with the division of exponents with the same base. The specific expression 3^10 / 3^4 can be simplified using this property. So, which property does this expression fall under?

When we encounter an expression that involves dividing exponents with the same base, we apply the property of the Quotient of Powers. In this case, the expression 3^10 / 3^4 can be simplified by subtracting the exponents, resulting in 3^(10-4) = 3^6.

This property states that when dividing two terms with the same base, you subtract the exponents to simplify the expression. It provides a shortcut for simplifying such calculations without the need to perform individual multiplications.

The Quotient Rule in calculus also utilizes a similar concept, where the derivative of a quotient is calculated by subtracting the derivative of the denominator from the derivative of the numerator, all divided by the square of the denominator.

Therefore, the correct answer to the question is that the expression 3^10 / 3^4 falls under the property of the Quotient of Powers in mathematics.

If you want to explore more about the Quotient of Powers and how it is applied in various mathematical problems, you can refer to additional resources such as textbooks or online tutorials.