Question

1. $2m^{3}p^{-8}q^{-5} \cdot 2m^{-1}q^{0}$

Explanation:

Step1: Multiply constant coefficients

$2 \times 2 = 4$

Step2: Combine $m$ terms (add exponents)

$m^{3} \cdot m^{-1} = m^{3 + (-1)} = m^{2}$

Step3: Keep $p$ term (no like terms)

$p^{-8}$ (remains unchanged)

Step4: Combine $q$ terms (add exponents)

$q^{-5} \cdot q^{0} = q^{-5 + 0} = q^{-5}$

Step5: Rewrite positive exponents (optional, standard form)

$q^{-5} = \frac{1}{q^5}$, $p^{-8} = \frac{1}{p^8}$

Answer:

$4m^{2}p^{-8}q^{-5}$ or $\frac{4m^2}{p^8q^5}$