%5E2.jpeg "(x^3y^4)^2")
Simplifying (x^3y^4)^2
In mathematics, simplifying expressions is a fundamental skill. One common type of expression involves exponents, and understanding how to handle them is crucial. This article will explore the simplification of the expression (x^3y^4)^2.
Understanding Exponents
An exponent indicates how many times a base number is multiplied by itself. In the expression x^3, 'x' is the base and '3' is the exponent, meaning 'x' is multiplied by itself three times (x * x * x).
Applying the Power of a Power Rule
The key to simplifying (x^3y^4)^2 is using the power of a power rule. This rule states that when raising a power to another power, you multiply the exponents.
In our case, we have:
- (x^3y^4)^2 = (x^3)^2 * (y^4)^2
Applying the power of a power rule to each term:
- (x^3)^2 = x^(3*2) = x^6
- (y^4)^2 = y^(4*2) = y^8
Therefore, the simplified expression is:
** (x^3y^4)^2 = x^6y^8**
Conclusion
By applying the power of a power rule, we effectively simplified the expression (x^3y^4)^2 to x^6y^8. This demonstrates the importance of understanding exponent rules for simplifying mathematical expressions.