Mathematics

Problem

Let

A = \dfrac{5^{3}\times 2^{-4}}{10^{-2}\times 5^{-1}}

. Answer the following: a. (i) Rewrite each power in

A

with a positive exponent. b. (ii) Simplify step by step to obtain a single power of

2

multiplied by a single power of

5

. c. (iii) Calculate the numerical value of

A

and express your answer in standard form (scientific notation).