%5E3.jpeg "(-4x^5y^3)^3")
Simplifying (-4x^5y^3)^3
This expression involves raising a product of a constant, variable, and another variable to a power. To simplify it, we'll use the following rules of exponents:
- (ab)^n = a^n * b^n: When a product is raised to a power, each factor is raised to that power.
- (a^m)^n = a^(m*n): When a power is raised to another power, the exponents are multiplied.
Step 1: Applying the first rule, we distribute the exponent 3 to each factor inside the parentheses:
(-4x^5y^3)^3 = (-4)^3 * (x^5)^3 * (y^3)^3
Step 2: Applying the second rule, we multiply the exponents for each variable:
(-4)^3 * (x^5)^3 * (y^3)^3 = -64 * x^(53) * y^(33)
Step 3: Simplifying the exponents:
-64 * x^(53) * y^(33) = -64x^15y^9
Therefore, the simplified form of (-4x^5y^3)^3 is -64x^15y^9.