Final answer:
The expression (7p⁻⁴ q⁸) (2p⁻³ q⁻²) simplifies to 14q⁶/p⁷ by multiplying coefficients and adding exponents, then moving terms with negative exponents to the denominator to ensure all exponents are positive.
Step-by-step explanation:
To simplify the expression (7p⁻⁴ q⁸) (2p⁻³ q⁻²) with positive exponents only, we first multiply the coefficients (7 and 2) and then apply the rule for multiplying exponents. When we multiply terms with exponents, we add the exponents if the base is the same. The general rule is xᵗʰ x⁹ = x(p+q).
Here's a step-by-step breakdown:
- Multiply the coefficients: 7 × 2 = 14.
- Add the exponents of p: (-4) + (-3) = -7.
- Add the exponents of q: 8 + (-2) = 6.
Combine the results with the bases:
14p⁻⁷ q¶
Since we want positive exponents only, we move p to the denominator:
14q¶ / p⁷
This result expresses the product of the two expressions with positive exponents.