Question

I am unable to understand how to solve this question, please send the working out.

Answer 1

Answer:

$(9x)^{\frac{1}{2} }.(8x^{\frac{-1}{2} })^{\frac{1}{3} }\\\\=9^{1/2}.x^{1/2}.8^{1/3}.x^{-1/2.1/3} \\\\=3.2.x^{1/2}.x^{-1/6} \\\\\\=6.x^{1/2-1/6}\\\\=6x^{1/3}$

Step-by-step explanation:

Answer 2

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
​
​​