%5E3.jpeg "(2ab^2)^3")
(2ab^2)^3: Understanding the Power of Exponents
Introduction
In algebra, exponents play a crucial role in simplifying complex expressions. One such expression is (2ab^2)^3, which may seem daunting at first, but fear not! In this article, we'll break it down and explore the power of exponents.
What is an Exponent?
An exponent is a small number that is raised to a power, indicating how many times a base number should be multiplied by itself. For example, in the expression 2^3, the 2 is the base, and the 3 is the exponent, indicating that 2 should be multiplied by itself three times: 2 × 2 × 2 = 8.
Breaking Down the Expression
Let's take a closer look at our expression: (2ab^2)^3. We can start by identifying the components:
- 2: the coefficient (a multiplier)
- a: a variable (a letter representing a value)
- b^2: a variable with an exponent (b squared)
- ^3: the exponent indicating the power to which the expression should be raised
Applying the Power Rule
When an expression is raised to a power, we can apply the power rule, which states that:
(xy)^n = x^n * y^n
In our case, we can apply this rule as follows:
(2ab^2)^3 = 2^3 \* (a)^3 \* (b^2)^3
Simplifying the Expression
Now, let's simplify each component:
- 2^3 = 8 (since 2 multiplied by itself three times is 8)
- (a)^3 = a^3 (the exponent 3 is applied to the variable a)
- (b^2)^3 = b^(2*3) = b^6 (the exponent 3 is applied to the expression b^2, resulting in b^6)
Putting it all together, we get:
(2ab^2)^3 = 8a^3b^6
And that's the simplified form of our original expression!
Conclusion
In conclusion, we've successfully broken down and simplified the expression (2ab^2)^3 using the power rule and basic exponent rules. By applying these rules, we can tame even the most complex expressions and uncover their underlying simplicity.
