Question

Evaluate: \[{(27)^{\dfrac{4}{3}}} + {(32)^{\dfrac{4}{5}}} + {(0.8)^{ - 1}}\]

Answer 1

Hint: In this question we need to evaluate the fractional powers of numbers and add them. Fractional powers may generally be simplified by identifying the squares and cubes of the numbers inside the bracket. This will save time and students need to have an idea about some cube and cube roots.

Complete answer:
Given equation is
\[{(27)^{\dfrac{4}{3}}} + {(32)^{\dfrac{4}{5}}} + {(0.8)^{ - 1}}\]
We can identify three terms 27, 32, 0.8 inside the brackets.
$
  27 = {3^3} \\
  32 = {2^5} \\
 $
Rewriting the given equation,
$
   = {({3^3})^{\dfrac{4}{3}}} + {({2^5})^{\dfrac{4}{5}}} + \left( {\dfrac{{10}}{8}} \right) \\
   \Rightarrow {3^4} + {2^4} + 1.25 \\
 $
Further solving we can get,
$
   = 81 + 16 + 1.25 \\
   = 98.25 \\
 $
Hence, the answer of \[{(27)^{\dfrac{4}{3}}} + {(32)^{\dfrac{4}{5}}} + {(0.8)^{ - 1}}\] is 98.25.

Note:
The exponentials are to be observed carefully. Try to be equipped with square square roots and some powers of small integers. This will increase the speed and accuracy of solving the problem.
Every time I try to reduce the problem into simpler form.