(a) Simplify the numerator and the denominator of the fraction (9p^ -2 q^ 3 )^ 5 2…

MATHEMATICS · Subjective · CBSE · Mathematics · Number Systems · Number Systems

Problem

(a) Simplify the numerator and the denominator of the fraction (9p−2q3)52(27p4q−6)−32\frac{(9p^{-2}q^{3})^{\tfrac{5}{2}}}{(27p^{4}q^{-6})^{-\tfrac32}} separately, writing each result with positive exponents. (b) Hence, simplify the entire fraction so that the final answer is expressed as a single product of powers of distinct primes and of the variables pp and qq, each with positive exponents only. (c) Find the value of the simplified fraction when p=13p=\dfrac13 and q=3q=3.

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