You must have JavaScript enabled to use this site.
Expand menu
menu_open
Minimize
Start chapters
Home
History
history
History
expand_more
{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics
equalizer
Progress
expand_more
Student
navigate_next
Teacher
navigate_next
filter_list
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
No results
{{ searchError }}
Choose book
search
cancel
menu_open
{{ courseTrack.displayTitle }}
{{ statistics.percent }}%
Sign in to view progress
{{ printedBook.courseTrack.name }}
{{ printedBook.name }}
Get free trial
search
Use offline
Tools
apps
Login
account_circle
menu_open
Rational Exponents and Radicals
Choose Course
Algebra 2
Radical Functions
Rational Exponents and Radicals
expand_more
close
Rational Exponents and Radicals 1.4 - Solution
arrow_back
Return to Rational Exponents and Radicals
To simplify the given expression, remember that the numerator of a
rational exponent
is the
exponent
of the expression, and the denominator is the
index
.
a
1
n
=
a
n
and
a
m
n
=
a
m
n
\begin{gathered} a^\frac{1}{{\color{#009600}{n}}}=\sqrt[{\color{#009600}{n}}]{a} \quad \text{ and } \quad a^\frac{{\color{#FF0000}{m}}}{{\color{#009600}{n}}}=\sqrt[{\color{#009600}{n}}]{a^{\color{#FF0000}{m}}} \end{gathered}
a
n
1
=
n
a
and
a
n
m
=
n
a
m
Let's simplify the expression!
(
x
3
)
5
2
\left(x^3\right)^\frac{5}{2}
(
x
3
)
2
5
MoveNumLeft
a
b
=
a
⋅
1
b
\dfrac{a}{b}=a\cdot \dfrac{1}{b}
b
a
=
a
⋅
b
1
(
x
3
)
5
⋅
1
2
\left(x^3\right)^{5\cdot \frac{1}{2}}
(
x
3
)
5
⋅
2
1
ProdInExponent
a
m
⋅
n
=
(
a
m
)
n
a^{m\cdot n}=\left(a^{m}\right)^{n}
a
m
⋅
n
=
(
a
m
)
n
(
(
x
3
)
5
)
1
2
\left(\left(x^3\right)^5 \right)^\frac{1}{2}
(
(
x
3
)
5
)
2
1
PowPow
(
a
m
)
n
=
a
m
⋅
n
\left(a^{m}\right)^{n}=a^{m\cdot n}
(
a
m
)
n
=
a
m
⋅
n
(
x
3
⋅
5
)
1
2
\left(x^{3\cdot5}\right)^{\frac{1}{2}}
(
x
3
⋅
5
)
2
1
Multiply
Multiply
(
x
15
)
1
2
\left(x^{15}\right)^{\frac{1}{2}}
(
x
1
5
)
2
1
a
1
2
=
a
a^{\frac{1}{2}}=\sqrt{a}
a
2
1
=
a
x
15
\sqrt{x^{15}}
x
1
5
