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 :

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

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

$=4^3/5^3$

$=64/125$

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