How do you simplify #4^-(5/2)#?

1 Answer
Jim G.
Jan 17, 2017

#1/32#

Explanation:

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

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(a^-mhArr1/a^m)color(white)(2/2)|)))#

#rArr4^(-5/2)=1/4^(5/2)#

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

#rArr4^(5/2)=(root(2)4)^5=(2)^5=32#

#rArr4^(-5/2)=1/4^(5/2)=1/32#

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