%5E3.jpeg "(2x^3y^4)^3")
(2x^3y^4)^3: A Powerful Expression
In algebra, we often encounter expressions involving variables and exponents. One such expression is (2x^3y^4)^3, which may seem complex at first, but can be simplified and understood with a few basic concepts.
Understanding Exponents
Before diving into the expression (2x^3y^4)^3, let's quickly review what exponents are. An exponent is a small number that indicates how many times a base number should be multiplied by itself. For example, in the expression 2^3, the base is 2, and the exponent is 3. This means we multiply 2 by itself three times: 2^3 = 2 × 2 × 2 = 8.
Expanding the Expression
Now, let's focus on (2x^3y^4)^3. To expand this expression, we need to apply the exponent rule, which states that when we raise a power to another power, we multiply the exponents.
(2x^3y^4)^3 = 2^3 × (x^3)^3 × (y^4)^3
Using the exponent rule, we get:
= 8x^9y^12
As you can see, the expression (2x^3y^4)^3 simplifies to 8x^9y^12.
Properties of Exponents
The expression (2x^3y^4)^3 demonstrates two important properties of exponents:
1. Product of Powers: When we raise a product to a power, we raise each factor to that power.
2. Power of a Power: When we raise a power to another power, we multiply the exponents.
These properties can be applied to various algebraic expressions, making it easier to simplify and manipulate them.
Conclusion
In conclusion, the expression (2x^3y^4)^3 is a powerful expression that can be simplified using the exponent rule. By understanding exponents and their properties, we can tackle complex algebraic expressions with confidence. Remember to apply the product of powers and power of a power rules to simplify expressions and unlock their secrets!
