Question

how to solve fraction exponent over 10??​

Answer 1

Answer:

${10}^{ - \frac{3}{5} } \times 0.5 \\ \\ = \frac{1}{ {10}^{ \frac{3}{5} } } \times 0.5 \\ \\ = \frac{1}{( {10}^{3} ) ^\frac{1}{5} } \times 0.5 \\ \\ = \frac{1}{ {1000}^{ \frac{1}{5} } } \times 0.5$

Now you can calculate exact value without calculator , if you know standard square root division method in that make group of 5 digits , but that will be two lengthy .

but we can get approximation quick

${2}^{5} = 64 \\ {3}^{5} = 243 \\ {4}^{5} = 512 \\ {5}^{5} = 3125$

So it is somewhere between 4 and 5 and near 4 .

I go with 4.2

$\approx\frac{1}{4.2} \times 0.5 \\ \\ = 0.119$

Calculator gives value

0.125

So we are pretty close .