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1 Move the negative sign to the left.
(
9
x
)
1
2
8
x
−
1
2
3
(9x)

2

1


3
√
8x
−
2

1





2 Convert
(
9
x
)
1
2
(9x)

2

1

to square root.
9
x
8
x
−
1
2
3
√
9x


3
√
8x
−
2

1





3 Use this rule:
a
b
=
a
b
√
ab

=√
a

√
b

.
9
x
8
x
−
1
2
3
√
9

√
x


3
√
8x
−
2

1





4 Since
3
×
3
=
9
3×3=9, the square root of
9
9 is
3
3.
3
x
8
x
−
1
2
3
3√
x


3
√
8x
−
2

1





5 Use Multiplication Distributive Property:
(
x
y
)
a
=
x
a
y
a
(xy)
a
=x
a
y
a
.
3
x
8
3
x
−
1
2
3
3√
x


3
√
8


3
√
x
−
2

1





6 Calculate.
3
x
×
2
x
−
1
2
3
3√
x

×2
3
√
x
−
2

1





7 Use this rule:
(
x
a
)
b
=
x
a
b
(x
a
)
b
=x
ab
.
3
x
×
2
x
−
1
2
×
3
3√
x

×2x

2×3

−1



8 Simplify
2
×
3
2×3 to
6
6.
3
x
×
2
x
−
1
6
3√
x

×2x

6

−1



9 Move the negative sign to the left.
3
x
×
2
x
−
1
6
3√
x

×2x
−
6

1



10 Use Negative Power Rule:
x
−
a
=
1
x
a
x
−a
=
x
a


1
.
3
x
×
2
×
1
x
6
3√
x

×2×

6
√
x



1


11 Use Quotient Rule:
x
a
x
b
=
x
a
−
b
x
b


x
a

=x
a−b
.
\[3\times 2\sqrt[2}-\frac{1}{6]{x}\]

12 Simplify
1
2
−
1
6
2

1
−
6

1
to
1
3
3

1
.
3
×
2
x
3
3×2
3
√
x



13 Simplify.
6
x
3
6
3
√
x