How do you simplify and write (3.89)^-5 * (3.89)^6(3.89)5(3.89)6 with positive exponents?

1 Answer
Jun 15, 2018

See a solution process below:

Explanation:

Use this rule of exponents: x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))xa×xb=xa+b

Substitute 3.893.89 for xx giving:

(3.89)^color(red)(-5) xx (3.89)^color(blue)(6) => 3.89^(color(red)(-5) + color(blue)(6)) => 3.89^1(3.89)5×(3.89)63.895+63.891

If necessary, we can further simplify the expression using this rule of exponents:

a^color(red)(1) = aa1=a

3.89^color(red)(1) = 3.893.891=3.89