Question

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

Answer 1

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}`