%5E4.jpeg "(-2x^2y^3)^4")
Simplifying the Expression (-2x²y³)^4
In mathematics, simplifying expressions involves rewriting them in their most basic form. Let's break down how to simplify the expression (-2x²y³)^4.
Understanding the Power of a Power Rule
The expression involves a power raised to another power. This requires us to apply the power of a power rule, which states:
(a^m)^n = a^(m*n)
In other words, when raising a power to another power, we multiply the exponents.
Applying the Rule
Let's apply the rule to our expression:
(-2x²y³)^4 = (-2)^4 * (x²)⁴ * (y³)⁴
Now, let's simplify each term:
- (-2)⁴ = 16 (Raising -2 to the fourth power gives us a positive value)
- (x²)⁴ = x⁸ (Multiplying the exponents)
- (y³)⁴ = y¹² (Multiplying the exponents)
The Simplified Expression
Combining all the simplified terms, we get the final result:
(-2x²y³)^4 = 16x⁸y¹²
Therefore, the simplified form of (-2x²y³)^4 is 16x⁸y¹².