91Ó°ÊÓ

Exponent rules are fundamental in simplifying expressions involving powers. A key rule is that any number raised to the power of 1 is itself.
So, \[ (-3)^{1} = -3 \].
Another important rule is that for any real number \(a\), the following holds true:
\[ a^{n} \times a^{m} = a^{n + m} \].
This means that when multiplying like bases, you add their exponents. Additionally, when a number is raised to another exponent, you multiply the exponents:
\[ (a^{n})^{m} = a^{n \times m} \].
Understanding and applying these rules can significantly simplify complex expressions. Practice using these rules to make problems manageable.

The zero exponent rule is a special but very useful rule in algebra. The rule states that any nonzero number raised to the power of zero is equal to one.
For instance:
\[ a^{0} = 1 \]
where \(a\) is any nonzero number.
This can be initially confusing, but it helps simplify expressions. Let’s look at an example.
Taking the expression \[ (-3)^{0} = 1 \] simplifies our original problem.
In general, always remember:

• Any number, no matter how big or small, when raised to zero equals 1.

This is universally true for nonzero values and is a powerful tool in algebraic manipulation.

Working with negative numbers can sometimes be tricky, but understanding the basics can help simplify problems. A negative number is any number less than zero, represented with a minus sign (-).
For example, -3 is a negative number.
When simplifying expressions, note the difference between negative numbers within and outside exponents. With our problem, initially, we see the expression \[ (-3)^{1} = -3 \].
Always maintain the negative sign along with the simplified value in such cases. Furthermore, when subtracting negative numbers, remember the rules of arithmetic involving negatives:

• Subtracting a negative number is akin to adding its positive counterpart.
• For instance, \[ -2 - (-5) = -2 + 5 = 3 \].

In our example problem, we ultimately subtract 1 from -3:
\[ -3 - 1 = -4 \].
This method is essential in achieving the correct simplified result.