%5E3-simplified.jpeg "(2x^2y^4)^3 Simplified")
Simplifying the Expression (2x^2y^4)^3
When working with exponential expressions, it's essential to understand the rules of exponents to simplify them. In this article, we'll explore how to simplify the expression (2x^2y^4)^3.
The Rule of Exponents
To simplify an expression with exponents, we need to recall the rule of exponents, which states that:
a^(mn) = (a^m)^n
This rule tells us that when we raise an exponential expression to a power, we can simplify it by raising the base to the power and then multiplying the exponents.
Simplifying the Expression
Now, let's apply the rule of exponents to simplify (2x^2y^4)^3.
(2x^2y^4)^3 = (2^3)(x^2)^3(y^4)^3
Using the rule of exponents, we can break down the expression into individual components:
- 2^3 = 8 (because 2 cubed equals 8)
- (x^2)^3 = x^(2*3) = x^6 (because the exponent 2 is multiplied by 3)
- (y^4)^3 = y^(4*3) = y^12 (because the exponent 4 is multiplied by 3)
Final Simplification
Now, let's combine the simplified components to get the final answer:
(2x^2y^4)^3 = 8x^6y^12
And that's it! We've successfully simplified the expression (2x^2y^4)^3 to 8x^6y^12.
I hope this article has helped you understand how to simplify exponential expressions using the rule of exponents.
