Answer 1

To find the product, we will use distributive law as follows:

\[0 . 1y\left( 0 . 1 x^5 + 0 . 1y \right)\]

\[ = \left( 0 . 1y \right)\left( 0 . 1 x^5 \right) + \left( 0 . 1y \right)\left( 0 . 1y \right)\]

\[ = \left( 0 . 1 \times 0 . 1 \right)\left( y \times x^5 \right) + \left( 0 . 1 \times 0 . 1 \right)\left( y \times y \right)\]

\[ = \left( 0 . 1 \times 0 . 1 \right)\left( x^5 \times y \right) + \left( 0 . 1 \times 0 . 1 \right)\left( y^{1 + 1} \right)\]

\[ = 0 . 01 x^5 y + 0 . 01 y^2\]

Thus, the answer is \[0 . 01 x^5 y + 0 . 01 y^2\].