Evaluate the following?

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1 Answer
Oct 26, 2016

Answer:

#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)#