Question

How do you simplify `\frac { 2^ { a } \cdot 2^ { 5} } { 2^ { b } }`?

Answer 1

See a solution process below:

Explanation:

First, simplify the numerator using this rule of exponents:

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

`(2^color(red)(a) * 2^color(blue)(5))/2^b = 2^(color(red)(a) + color(blue)(5))/2^b`

Next, use this rule of exponents to simplify the numerator and denominator:

`a^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))`

`2^color(red)(a + 5)/2^color(blue)(b) = 2^(color(red)(a + 5)-color(blue)(b))`