Final answer:
To simplify the expression (p^(-9)q^(5))/(p^(5)q^(-3)), rules of exponents are applied. The final simplified form without negative exponents is 1/(p^14)*q^8.
Step-by-step explanation:
To simplify the expression (p^(-9)q^(5))/(p^(5)q^(-3)), we apply the rules of exponents. The rule for division is a^m / a^n = a^(m-n). So for the p term, we subtract the exponent in the denominator from the exponent in the numerator: -9 - 5 = -14, and for the q term, we subtract the exponent in the denominator from the exponent in the numerator: 5 - (-3) = 8.
However, we want the answer without any negative exponents. The rule for changing the sign of an exponent is a^(-n) = 1/a^n, so we apply this rule to p^-14 to get 1/p^14 . Thus, the simplified form of the expression is 1/(p^14)*q^8.
Learn more about Simplifying Exponential Expressions