Question

1. fully simplify: $(2x^{2}y^{4})^{5}$

Explanation:

Step1: Apply power of a product rule

Distribute the exponent to each term inside the parentheses:
$(2x^2y^4)^3 = 2^3 \cdot (x^2)^3 \cdot (y^4)^3$

Step2: Calculate each exponential term

Compute the powers:
$2^3 = 8$, $(x^2)^3 = x^{2 \times 3} = x^6$, $(y^4)^3 = y^{4 \times 3} = y^{12}$

Step3: Combine the simplified terms

Multiply the results together:
$8 \cdot x^6 \cdot y^{12}$

Answer:

$8x^6y^{12}$