How can patterns be used to determine products of a number and a power of 10?

Patterns used to determine the product of a number and a power of 10 :

When we multiply a number by a positive exponent of 10 then the resultant number is obtained by putting 0's, equal to the exponent, after the number.

For example :

2 × 10 = 20

2 × 10² = 200,

2 × 10³ = 2000,

so on

In other words, we add zeros as much as the power of 10 after the number in the resultant number.

(5x-1)^2= (5x)^2-2(5x)×1+(1)^2=25x^2-10x+1