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Simplifying expressions is all about making a math problem easier to solve. It involves breaking down complex expressions into simpler parts. In the example given, \((-5)^{4}\), we simplified it step-by-step to find its value.

This process started with understanding what \((-5)^{4}\) actually means. It means that -5 is multiplied by itself 4 times. When we express it like this: \(-5 \times -5 \times -5 \times -5\), it becomes easier to handle.

Multiplying in pairs can help simplify further. First, you multiply the first two -5s together, and then the next two. Finally, you multiply the results of these pairs together. Voila! You get the simplified answer: 625.

Negative numbers can be tricky, but they're essential in math. A negative number is simply a number with a minus sign in front of it. When you're dealing with exponentiation, it's crucial to understand how negative numbers behave.

For the expression \((-5)^{4}\), you might wonder why the result isn't negative. That's because when you multiply two negative numbers, the result is positive.

Here's a quick breakdown:

• \-5 \times -5 = 25\.
• \-5 \times -5 = 25\.

Then, when you multiply the two positive results (25 \times 25), you get 625. So, even though we started with a negative number, the final answer is positive because of the even exponent.

When we talk about powers in math, we're referring to a number multiplied by itself a certain number of times. The little number up high (the exponent) tells you how many times to multiply the base number. In our example, the base number is -5, and the exponent is 4.

Here's a breakdown:

• The base number is -5.
• The exponent is 4.

So, \(-5^4\) means \-5 \times -5 \times -5 \times -5\.

The cool thing about powers is they let you manage large numbers or repeated multiplication easily. Imagine if you had to write out \(-5\) multiplied by itself 20 times! It would be much simpler to write \((-5)^{20}\).

Remember: When the exponent is even, and the base is negative, like in this exercise, the final answer will be positive. This is because a negative times a negative is always a positive.