Answer:
27.
Step-by-step explanation:
It is one property of exponents that for any numbers a, b, and c
[tex](a^b)^c=a^{bc}[/tex]
Therefore, using this property the expression [tex](9^7) ^{3/14}[/tex] becomes
[tex](9^7) ^{3/14} =9^{(7*\frac{3}{14} )}[/tex].
and when when simplify the exponents, we get:
[tex]9^{(\frac{21}{14} )}= 9^{\frac{3}{2} }= (9^{\frac{1}{2} })^3[/tex].
Since for any number [tex]a^\frac{1}{2} =\sqrt{a}[/tex] ( [tex]\dfrac{1}{2}[/tex] in the exponent means the square root) , [tex](9^{\frac{1}{2} })^3[/tex] is rewritten as
[tex](\sqrt9} )^3[/tex]
which simplifies to
[tex](\sqrt9} )^3=3^3 =\bold{27}[/tex]
Thus,
[tex]\boxed{ (9^7) ^{3/14}=27}[/tex]
