%5E2.jpeg "(b^7)^2")
Simplifying Exponential Expressions: (b^7)^2
In mathematics, especially in algebra, we frequently encounter expressions involving exponents. One such expression is (b^7)^2. Understanding how to simplify this expression is crucial for various mathematical operations.
Understanding the Rules of Exponents
The key to simplifying this expression lies in understanding the following rule of exponents:
(a^m)^n = a^(m*n)
This rule states that when raising a power to another power, we multiply the exponents.
Applying the Rule to (b^7)^2
Applying the rule to our expression, we get:
(b^7)^2 = b^(7*2) = b^14
Therefore, (b^7)^2 simplifies to b^14.
Conclusion
Simplifying expressions like (b^7)^2 is essential for solving equations, manipulating algebraic expressions, and understanding the relationships between variables in various mathematical contexts. By applying the basic rules of exponents, we can effectively simplify these expressions and gain a deeper understanding of their underlying structure.