Question

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

Explanation:

Step1: Multiply the coefficients

$2 \times 2 = 4$

Step2: Combine like terms for $m$

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

Step3: Keep the $p$ term unchanged

$p^{-8}$ (no like terms to combine)

Step4: Combine like terms for $q$

$q^{-5} \cdot q^{0} = q^{-5 + 0} = q^{-5} = \frac{1}{q^{5}}$

Step5: Combine all simplified terms

$4 \cdot m^{2} \cdot p^{-8} \cdot \frac{1}{q^{5}} = \frac{4m^{2}}{p^{8}q^{5}}$

Answer:

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