n=288
Step-by-step explanation:
Rewrite the equation as Β
β
n
=
18
β
8
β
8
β
18
.
β
n
=
18
β
8
β
8
β
18
To remove the radical on the left side of the equation, square both sides of the equation.
βn
2
=
(
18
β
8
β
8
β
18
)
2
Simplify each side of the equation. Β
Use Β
n
β
a
x
=
a
x
n
to rewrite Β
β
n Β as Β n
1
2
.
(
n
1
2
)
2
=
(
18
β
8
β
8
β
18
)
2
Simplify Β
(
n
1
2
)
2
. Β
Multiply the exponents in Β
(
n
1
2
)
2
. Β
Apply the power rule and multiply exponents, Β
(
a
m)n
=
a
m
n
.
n
1
2
β
2
=
(
18
β
8
β
8
β
18
)
2
Cancel the common factor of Β 2 Β
Cancel the common factor.
n
1
2
β
2
=
(
18
β
8
β
8
β
18
)
2
Rewrite the expression.
n
1
=
(
18
β
8
β
8
β
18
)
2
Simplify.
n
=
(
18
β
8
β
8
β
18
)
2
Simplify Β
(
18
β
8
β
8
β
18
)
2
Simplify each term.
Rewrite Β
8 Β as Β 2
2
β
2
. Β
Factor Β
4 Β out of Β 8 Β
n
=
(
18
β
4
(
2
)
β
8
β
18
)
2
Rewrite Β
4 Β as Β 2
2 Β
n
=
(
18β
2
2
2
β
8
β
18
)
2
Pull terms out from under the radical.
n
=
(
18
(
2
β
2
)
β
8
β
18
)
2
Multiply Β
2 Β by Β 18 Β
n
=
(
36
β
2
β
8
β
18
)
2
Rewrite Β
18
as Β
3
2
β
2
.
Factor Β
9
out of Β
18
.
n
=
(
36
β
2
β
8
β
9
(
2
)
)
2
Rewrite Β
9
as Β
3
2
.
n
=
(
36
β
2
β
8
β
3
2
β
2
)
2
Pull terms out from under the radical.
n
=
(
36
β
2
β
8
(
3
β
2
)
)
2
Multiply Β
3
by Β
β
8
.
n
=
(
36
β
2
β
24
β
2
)
2
Simplify terms.
Subtract Β
24
β
2
from Β
36
β
2
.
n
=
(
12
β
2
)
2
Simplify the expression.
Apply the product rule to Β
12
β
2
.
n
=
12
2
β
2
2
Raise Β
12
to the power of Β
2
.
n
=
144
β
2
2
Rewrite Β
β
2
2
as Β
2
.
Use Β
n
β
a
x
=
a
x
n
to rewrite Β
β
2
as Β
2
1
2
.
n
=
144
(
2
1
2
)
2
Apply the power rule and multiply exponents, Β
(
a
m
)
n
=
a
m
n
.
n
=
144
β
2
1
2
β
2
Combine Β
1
2
and Β
2
.
n
=
144
β
2
2
2
Cancel the common factor of Β
2
.
Cancel the common factor.
n
=
144
β
2
2
2
Rewrite the expression.
n
=
144
β
2
1
Evaluate the exponent.
n
=
144
β
2
Multiply Β
144
by Β
2
.
n
=
288