Question

1. write a simplified expression using exponents. (4z^4)^2 = 8z^8

Explanation:

Step1: Apply power - of - a - product rule

$(ab)^n=a^n\times b^n$. Here, $(4z^{4})^{2}=4^{2}\times(z^{4})^{2}$.

Step2: Calculate $4^{2}$ and apply power - of - a - power rule

$4^{2}=16$, and $(z^{4})^{2}=z^{4\times2}=z^{8}$ according to $(a^{m})^{n}=a^{mn}$.

Step3: Multiply the results

$16\times z^{8}=16z^{8}$

Answer:

$16z^{8}$