Question

Evaluate the following?

Answer 1

`x^(77/15)=root(15)(x^(77))`

Explanation:

Using the `color(blue)"laws of exponents"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(a^(m/n)=root(n)(a^m))color(white)(2/2)|)))`

and `color(red)(bar(ul(|color(white)(2/2)color(black)(a^mxxa^n=a^(m+n) , a^m/a^n=a^(m-n) ,a^-mhArr1/a^m)color(white)(2/2)|)))`

The above expression can be written as.

`x^(3/2)xxx^(5/3)xxx^(77/30)xxx^(-3/5)`

`=x^(3/2+5/3+77/30-3/5)`

This now becomes a fraction exercise. That is.

`3/2+5/3+77/30-3/5`

`=45/30+50/30+77/30-18/30=154/30=77/15`

Thus our simplification is.

`x^(77/15)=root(15)(x^(77)`