%5E4.jpeg "(x^2y^3)^4")
Understanding (x^2y^3)^4
This expression involves exponents and power of a product. Let's break it down step-by-step.
Exponents Explained
- Base: The base is the number or variable being multiplied by itself. In this case, the bases are x and y.
- Exponent: The exponent tells you how many times to multiply the base by itself. Here, we have 2 and 3 as exponents for x and y, respectively.
- Power: The entire expression (x^2y^3) is raised to the power of 4. This means we are multiplying the entire expression by itself four times.
Applying the Rules
To simplify this, we use the following rules:
1. Power of a Product: When raising a product to a power, you raise each factor to that power.
- (x^2y^3)^4 = (x^2)^4 * (y^3)^4
2. Power of a Power: When raising a power to another power, you multiply the exponents.
- (x^2)^4 = x^(2*4) = x^8
- (y^3)^4 = y^(3*4) = y^12
Therefore, the simplified expression is:
(x^2y^3)^4 = x^8y^12
In Conclusion
Simplifying (x^2y^3)^4 is a straightforward process using the basic rules of exponents. By applying the power of a product and power of a power rules, we arrive at the simplified form x^8y^12.