Question

1. $(4r^4)^2$

Explanation:

Step1: Apply power of a product rule

$(ab)^n = a^n b^n$, so $(4r^4)^2 = 4^2 \cdot (r^4)^2$

Step2: Calculate numerical term

$4^2 = 16$

Step3: Apply power of a power rule

$(a^m)^n = a^{m \cdot n}$, so $(r^4)^2 = r^{4 \times 2} = r^8$

Step4: Combine the results

Multiply the numerical and variable terms: $16 \cdot r^8$

Answer:

$16r^8$