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What is the value of (9^7) ^3/14, in simplest terms? a0

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2 votes

Answer:

27.

Explanation:

It is one property of exponents that for any numbers a, b, and c


(a^b)^c=a^(bc)

Therefore, using this property the expression
(9^7) ^(3/14) becomes


(9^7) ^(3/14) =9^{(7*(3)/(14) )}.

and when when simplify the exponents, we get:


9^{((21)/(14) )}= 9^{(3)/(2) }= (9^{(1)/(2) })^3.

Since for any number
a^(1)/(2) =√(a) (
(1)/(2) in the exponent means the square root) ,
(9^{(1)/(2) })^3 is rewritten as


(\sqrt9} )^3

which simplifies to


(\sqrt9} )^3=3^3 =\bold{27}

Thus,


\boxed{ (9^7) ^(3/14)=27}

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