%5E4.jpeg "(2y^3)^4")
(2y^3)^4: Understanding the Exponent Rule
In algebra, exponent rules play a crucial role in simplifying expressions and solving equations. One of the most commonly used exponent rules is the power of a power rule, which states that (a^m)^n = a^(mn). In this article, we will explore how to apply this rule to simplify the expression (2y^3)^4.
The Power of a Power Rule
Before diving into the simplification of (2y^3)^4, let's take a quick look at the power of a power rule. This rule states that when an expression with an exponent is raised to another power, the result is an expression with an exponent that is the product of the two exponents.
(a^m)^n = a^(mn)
For example, (2^2)^3 can be simplified using this rule as follows:
(2^2)^3 = 2^(2*3) = 2^6
Simplifying (2y^3)^4
Now, let's apply the power of a power rule to simplify (2y^3)^4.
(2y^3)^4 = (2^1*y^3)^4
Using the power of a power rule, we can rewrite the expression as:
2^(1*4) * (y^3)^4
= 2^4 * y^(3*4)
= 2^4 * y^12
= 16y^12
Therefore, (2y^3)^4 can be simplified to 16y^12.
Conclusion
In this article, we have seen how to apply the power of a power rule to simplify the expression (2y^3)^4. By understanding this rule, we can simplify complex expressions and make algebraic manipulations easier.
