%5E2.jpeg "(a^3b)^2")
Understanding (a³b)²
In mathematics, simplifying expressions is crucial for understanding their value and relationships. One such expression is (a³b)². Let's break down this expression and explore its simplification.
The Power of a Power
The expression (a³b)² involves two key concepts:
- Exponents: The superscript "2" in (a³b)² indicates that the entire expression within the parentheses is being multiplied by itself.
- Power of a Power: The expression a³b itself has a power, which is "3" for "a" and "1" for "b".
Simplifying the Expression
To simplify (a³b)², we can apply the rule of power of a power:
(x^m)^n = x^(m*n)
Applying this rule to our expression:
- (a³b)² = (a³)² * (b¹)²
- = a^(32) * b^(12)
- = a⁶ * b²
Therefore, the simplified form of (a³b)² is a⁶b².
Example:
Let's assume a = 2 and b = 3.
- (a³b)² = (2³ * 3)²
- = (8 * 3)²
- = 24²
- = 576
Now, let's calculate a⁶b² using the same values:
- a⁶b² = 2⁶ * 3²
- = 64 * 9
- = 576
As you can see, both expressions result in the same value, confirming that our simplification is correct.
Conclusion
Simplifying expressions like (a³b)² allows us to better understand their value and how they relate to other mathematical concepts. By applying the rules of exponents, we can effectively simplify these expressions and perform further calculations with ease.