Final answer:
The simplified form of the expression (10x⁻⁵y⁴z⁻³)/(5x⁸y⁻⁹) using only positive exponents is 2x³y¹³/z³.
Step-by-step explanation:
Simplifying the Expression with Positive Exponents
The original question asks us to simplify the expression (10x⁻⁵y⁴z⁻³)/(5x⁸y⁻⁹) and write the answer using only positive exponents. To simplify this expression, we apply the properties of exponents, where we subtract exponents when dividing like bases and write expressions with negative exponents as their reciprocals to get positive exponents. Using these rules, let's simplify the expression step by step.
Step 1: Factor the numerical coefficients and split the variables: (10/5) × (x⁻⁵/x⁸) × (y⁴/y⁻⁹) × z⁻³.
Step 2: Simplify the numerical coefficients and apply the exponent rules: (2) × x⁻⁵⁵⁸ × y⁴⁻⁹ × z⁻³.
Step 3: Subtract the exponents of like bases: 2 × x³ × y¹³ × (1/z³).
Step 4: Rewrite with only positive exponents: 2x³y¹³/z³.
Thus, the simplified expression with only positive exponents is 2x³y¹³/z³.