Question

1. $(2x^{0}y^{2})^{4}$

Explanation:

Step1: Simplify $x^0$ (zero exponent rule)

Any non-zero number to the power of 0 is 1, so $x^0 = 1$.
The expression becomes: $(2 \cdot 1 \cdot y^2)^4 = (2y^2)^4$

Step2: Apply power of a product rule

Distribute the exponent 4 to each factor: $2^4 \cdot (y^2)^4$

Step3: Calculate each term

$2^4 = 16$; use power of a power rule: $(y^2)^4 = y^{2 \times 4} = y^8$
Combine terms: $16 \cdot y^8$

Answer:

$16y^8$