%5E4-expanded-form.jpeg "(-3x)^4 Expanded Form")
Expanding (-3x)^4: A Step-by-Step Guide
When dealing with algebraic expressions, it's essential to know how to expand powers of variables and constants. In this article, we'll focus on expanding the expression (-3x)^4 and break it down into its simplest form.
What is the Power Rule?
Before we dive into expanding (-3x)^4, let's take a quick look at the power rule. The power rule is a fundamental concept in algebra that states:
a^n = a × a × a × ... (n times)
In other words, when you raise a number or variable to a power n, you multiply it by itself n times.
Expanding (-3x)^4
Now, let's apply the power rule to (-3x)^4. To expand this expression, we need to multiply -3x by itself four times.
Step 1: -3x × -3x = 9x^2
Step 2: 9x^2 × -3x = -27x^3
Step 3: -27x^3 × -3x = 81x^4
And that's it! We've successfully expanded (-3x)^4 to its simplest form, which is 81x^4.
Conclusion
Expanding algebraic expressions like (-3x)^4 can seem daunting at first, but by applying the power rule and following a step-by-step approach, you can break it down to its simplest form. Remember to multiply the base -3x by itself four times, and you'll arrive at the correct answer: 81x^4.
Practice Time!
Try expanding these expressions on your own:
(2x)^3(-2y)^5(3z)^2
Do you have any questions or need help with a specific problem? Feel free to ask!
