Simplify the following expressions in index form: a) 7a imes 2a2 b) p3 imes 2p5 imes 8p4 c) z4 imes z4

Recall that $a = a^1$. When multiplying terms with the same base, add their exponents ($x^m \times x^n = x^{m+n}$).

$$a^1 \times a^2 = a^{1+2} = a^3$$

$$14 \times a^3 = 14a^3$$

The simplified expression is $\boxed{14a^3}$.

When multiplying terms with the same base, add their exponents ($x^m \times x^n = x^{m+n}$).

$$p^3 \times p^5 \times p^4 = p^{3+5+4} = p^{12}$$

$$16 \times p^{12} = 16p^{12}$$

The simplified expression is $\boxed{16p^{12}}$.

$x^m \div x^n = x^{m-n}$.

$$z^4 \div z^4 = z^{4-4} = z^0$$

$$z^0 = 1$$

The simplified expression is $\boxed{1}$.