How do you simplify #(16/25)^(3/2)#?

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Answer 1 · 2016-02-07T18:39:03

#64/125#

Remember that #x^(3/2)=sqrt(x)^3#

With this in mind we can re-write the above expression as:

#(16/25)^(3/2) = sqrt(16/25)^3#

Don't forget that #16# and #25# are square numbers so by taking their square root we can cancel the radical sign over the fraction to get:

#(4/5)^3#

And now simply cube the numbers inside the brackets:

#(4/5)^3 = 64/125#

Answer 2 · 2016-02-07T18:41:13

#64/125#

I shall apply the following 2 laws of exponents :

#therefore (16/25)^(3/2)=(16^(3/2))/25^(3/2)#

#=sqrt(16^3)/sqrt(25^3)#

#=4^3/5^3#

#=64/125#