Question

Simplify \[\dfrac{125\times {{8}^{3}}\times 1000}{8\times {{5}^{3}}\times {{10}^{2}}}\] ?

Answer 1

Hint: Such questions are quite straightforward and are very easy to solve. This particular problem can be solved very efficiently once we get all the underlying concepts behind the question. We need to have a fair amount of ideas of fractions and simplification of fractions. In this particular problem and problems similar to this, we first of all need to check the common terms that are present on the numerator as well as the denominator. After this we need to cancel such terms and then proceed with the problem. The final result that shall be obtained here should be of the simplest form.

Complete step by step answer:
Now we start off with the solution to the above given problem by first trying to identify all the common terms which are present on the numerator as well as on the denominator. First we need to remove all the power terms and rewrite the equation as,
\[\dfrac{125\times 512\times 1000}{8\times 125\times 100}\]
 On close observation, we can figure out that \[125,8,100\] are the terms that are present on both the numerator and the denominator. So we cancel out these terms and the simplest form would be equal to \[64\times 10\], which turns out to be equal to \[640\]. This cannot be further simplified down, hence our answer to the problem is \[640\] .

Note: In such problems we need to have some fair amount of knowledge of fractions, rational and irrational numbers. We need to be very careful and extremely cautious while we find the common terms on both the numerator and the denominator as this task is prone to a lot of mistakes. The final answer should be of the simplest form, if not we need to simplify it further.