Question

question
fully simplify.
\\((-5x^4y^4)^3\\)
answer attempt 1 out of 2

Explanation:

Step1: Apply power of a product rule

Distribute the exponent 3 to each factor inside the parentheses:
$$(-5)^3 \cdot (x^4)^3 \cdot (y^4)^3$$

Step2: Calculate each factor

Compute the numerical term and apply power of a power rule ($(a^m)^n=a^{m \cdot n}$):
$$(-5)^3 = -125, \quad (x^4)^3 = x^{4 \cdot 3}=x^{12}, \quad (y^4)^3 = y^{4 \cdot 3}=y^{12}$$

Step3: Combine the factors

Multiply the simplified terms together:
$$-125 \cdot x^{12} \cdot y^{12}$$

Answer:

$-125x^{12}y^{12}$