Question

How do you simplify `(m^7)^4*m^3` and write it using only positive exponents?

Answer 1

See the entire simplification process below:

Explanation:

First, use this rule for exponents to simplify the term on the left:

`(x^color(red)(a))^color(blue)(b) = x^(color(red)(a)xxcolor(blue)(b))`

`(m^color(red)(7))^color(blue)(4)m^3 = m^(color(red)(7)xxcolor(blue)(4))m^3 = m^28m^3`

Now, use this rule of exponents to complete the simplification:

`x^color(red)(a)x^color(blue)(b) = x^(color(red)(a)+color(blue)(b))`

`m^color(red)(28)m^color(blue)(3) = m^(color(red)(28)+color(blue)(3)) = m^31`