Final answer:
To simplify the expression (m¹⁰n¹²ps⁸)/(mn⁵s⁵), we cancel out like terms and subtract exponents, yielding the simplest form m⁹n⁷ps³.
Step-by-step explanation:
To simplify the expression (m¹⁰n¹²ps⁸)/(mn⁵s⁵), we need to cancel out common terms in the numerator and the denominator using the property of exponents that states a⁺/ₙ⁺ = a⁻¹¹, where a is the base and m and n are the exponents. The variables m and n appear in both the numerator and the denominator, so we subtract the exponents in the denominator from those in the numerator for each:
- For m: m¹⁰/m = m⁹
- For n: n¹²/n⁵ = n⁷
- For s: s⁸/s⁵ = s³
There is one term p in the numerator without a corresponding term in the denominator, so it remains as is. Therefore, the expression in simplest form is m⁹n⁷ps³, which corresponds to option C.