Question

How do you simplify `b^ { 4} \cdot b ^ { 7} \cdot b ^ { 5}`?

Answer 1

See a solution process below:

Explanation:

Use this rule for exponents to simplify the expression:

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

`b^color(red)(4) xx b^color(blue)(7) xx b^color(green)(5) => b^(color(red)(4) + color(blue)(7) + color(green)(5)) => b^16`

Answer 2

This is a law of exponents
`a^mxxa^n=a^(m+n)`
Similarly
`a^mxxa^nxxa^p=a^(m+n+p)`
`a` here in the problem `b`
and `m,n,p` are `4,7,5`
So....
`b^4xxb^7xxb^5=b^(4+7+5)`
Which gives
`b^16`