Question

Sonia knows that the cube root of
x
can be written as
x
1
3
. Which is the BEST explanation of why that is true?


Since
(
x
m
)
n
=
x
m
n
,
(
x
1
3
)
3
=
x
.


Since
(
x
m
)
n
=
x
m
n
,
(
x
3
)
1
3
=
x
.


Since
(
x
m
)
(
x
n
)
=
x
m
n
,
(
x
1
3
)
(
x
3
)
=
x
.


Since
(
x
m
)
(
x
n
)
=
x
m
+
n
,
(
x
1
3
)
(
x
3
)
=
x
.

Answer 1

Option 1.

Reason: The cube root of x is the number that when raised to the third power gives x. Using (x^m)^n = x^{mn}, we have (x^{1/3})^3 = x^{(1/3)·3} = x, so x^{1/3} is the cube root of x.