%5E4.jpeg "(-2x^5y^3)^4")
Simplifying (-2x^5y^3)^4
This expression involves raising a product of terms with exponents to another power. To simplify it, we use the following rules of exponents:
1. Power of a Product: (ab)^n = a^n * b^n 2. Power of a Power: (a^m)^n = a^(m*n)
Let's break down the simplification step-by-step:
Step 1: Apply the Power of a Product rule.
(-2x^5y^3)^4 = (-2)^4 * (x^5)^4 * (y^3)^4
Step 2: Apply the Power of a Power rule.
(-2)^4 * (x^5)^4 * (y^3)^4 = 16 * x^(54) * y^(34)
Step 3: Simplify the exponents.
16 * x^(54) * y^(34) = 16x^20y^12
Therefore, the simplified expression for (-2x^5y^3)^4 is 16x^20y^12.