How to Solve x³ x⁵: A Simple Guide to Exponent Rules
This guide will walk you through solving the equation x³ x⁵, focusing on understanding the fundamental rules of exponents. Understanding these rules is crucial for mastering algebra and many other mathematical concepts.
Understanding Exponents
Before we dive into the solution, let's quickly review what exponents represent. An exponent tells you how many times a base number is multiplied by itself. For example:
- x² means x * x
- x³ means x * x * x
- x⁵ means x * x * x * x * x
The Rule for Multiplying Exponents with the Same Base
The key to solving x³ x⁵ lies in understanding the rule for multiplying exponential expressions with the same base. This rule states:
xᵃ * xᵇ = x⁽ᵃ⁺ᵇ⁾
In other words, when multiplying terms with the same base (in this case, 'x'), you simply add the exponents.
Solving x³ x⁵
Now let's apply this rule to our problem:
x³ x⁵ = x⁽³⁺⁵⁾ = x⁸
Therefore, the solution to x³ x⁵ is x⁸.
Practice Problems
To solidify your understanding, try solving these similar problems:
- y⁴ * y²
- a⁶ * a³
- z² * z⁵ * z
Remember, the key is to identify the common base and then add the exponents.
Beyond the Basics: Division and Other Exponent Rules
While this guide focused on multiplication, remember that there are other important rules governing exponents, including:
- Division: xᵃ / xᵇ = x⁽ᵃ⁻ᵇ⁾ (Subtract the exponents when dividing terms with the same base)
- Power of a Power: (xᵃ)ᵇ = x⁽ᵃ*ᵇ⁾ (Multiply the exponents when raising a power to another power)
- Zero Exponent: x⁰ = 1 (Any non-zero base raised to the power of zero equals 1)
- Negative Exponent: x⁻ᵃ = 1/xᵃ (A negative exponent means to take the reciprocal)
Mastering these exponent rules will significantly improve your ability to manipulate and solve algebraic equations. Keep practicing, and you'll quickly become proficient!
