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The power rule is a fundamental principle used in simplifying exponential expressions. It provides a way to handle expressions where both the numerator and the denominator are raised to a power. In simple terms, if you have a fraction like \((a/b)^n\), you can separate the expression into \(a^n / b^n\).

This rule is particularly useful because it allows us to break down complex expressions step by step, making them easier to manage. For example, in the given problem, we have \((-6/y)^3\). The power rule enables us to rewrite this as \((-6)^3 / y^3\). By applying the power rule, we can individually manage the base \((-6)\) and the variable \(y\).

Consider this rule as a technique to distribute the power across both the numerator and the denominator of a fraction. This ensures consistency and helps in simplifying and evaluating the expression more efficiently.

Simplifying expressions involves reducing the expression to its most basic form without changing its value. The goal is to make the expression as clear and concise as possible. By applying the power rule, we can simplify expressions such as \((-6/y)^3\) to \((-6)^3 / y^3\).

After breaking it down using the power rule, simplify further by calculating powers. With \((-6)^3\), simply multiply \(-6\) by itself three times: \((-6) \times (-6) \times (-6) = -216\).

Now, your expression becomes \(-216 / y^3\). It’s essential to leave the result in this form if \(y\)'s specific value isn't known. However, once you know \(y\), substitute and evaluate to simplify the expression entirely.

• Use the power rule to separate the base and exponent.
• Calculate individual powers.
• Simplify the expression based on known values.

Exponents are a way of expressing how many times a number, known as the base, is multiplied by itself. For instance, \(a^n\) means that the base \(a\) is used as a factor \(n\) times. Mastering the concept of exponents is crucial, as it applies to numerous areas of mathematics and science.

In the exercise, we work with the exponent 3 in \((-6/y)^3\). This indicates that both \(-6\) and \(y\) are multiplied by themselves three times. This repetition showcases the power of exponents in expressing large numbers straightforwardly without extensive multiplication signs.

Remember:

• An exponent applies to everything within the parentheses.
• Negative bases raised to an odd number of times remain negative, as shown in \((-6)^3\).
• In fractions, apply the exponent to both numerator and denominator separately.

Recognizing how exponents work will allow you to understand not only simplifying tasks but also more advanced mathematical concepts that build on this foundation.