A rectangular box has the following dimensions: length m

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

Problem

A rectangular box has the following dimensions: length = (23×5x)1/2 =\,(2^{3}\times5x)^{1/2}\, m, breadth = (2x2y−3)3/2 =\,(2x^{2}y^{-3})^{3/2}\, m, and height = (x410y)−1 =\,\left(\dfrac{x^{4}}{10y}\right)^{-1}\, m. (a) Express each dimension with positive exponents only. (b) Determine the volume of the box in simplest form as a product of powers of distinct primes and of the variables xx and yy, using only positive exponents.

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