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

Question

asked Mar 7, 2020 165k views

1 Answer

Nazer · Answer 1 · 2020-03-13T04:16:18+0000

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,

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