Question

How do you evaluate `\frac { 8^ { 5} \cdot 7^ { 8} } { 8^ { 7} \cdot 7^ { 2} }`?

Answer 1

See a solution process below:

Explanation:

First, use these two rules of exponents to simplify the expression:

`x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))` and `x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))`

`(8^color(red)(5) * 7^color(red)(8))/(8^color(blue)(7) * 7^color(blue)(2)) => 1/8^(color(blue)(7)-color(red)(5)) * 7^(color(red)(8)-color(blue)(2)) => 1/8^2 * 7^6 => 7^6/8^2`

Now, execute the exponent operations:

`7^6/8^2 = 117649/64`