%5E3.jpeg "(2x^5y^2)^3")
Simplifying (2x^5y^2)^3
In mathematics, simplifying expressions is a fundamental skill. Here's how to simplify the expression (2x^5y^2)^3:
Understanding the Exponent Rule
The expression (2x^5y^2)^3 means we're multiplying the entire term (2x^5y^2) by itself three times:
(2x^5y^2)^3 = (2x^5y^2) * (2x^5y^2) * (2x^5y^2)
A key rule of exponents states that when raising a product to a power, you raise each factor to that power. In other words:
(ab)^n = a^n * b^n
Applying the Rule
Using this rule, let's break down our expression:
- Raise the coefficient to the power: 2^3 = 8
- Raise each variable to the power: (x^5)^3 = x^(5*3) = x^15
- Raise the other variable to the power: (y^2)^3 = y^(2*3) = y^6
The Simplified Expression
Putting it all together, the simplified expression becomes:
(2x^5y^2)^3 = 8x^15y^6
Therefore, (2x^5y^2)^3 simplifies to 8x^15y^6.