1 Use this rule:
a
b
=
a
b
\sqrt{ab}=\sqrt{a}\sqrt{b}
√
ab
=√
a
√
b
x
3
2
3
\sqrt{{x}^{3}}\sqrt{23}
√
x
3
√
23
2 Simplify
x
3
\sqrt{{x}^{3}}
√
x
3
to
(
x
3
)
1
2
{({x}^{3})}^{\frac{1}{2}}
(x
3
)
2
1
(
x
3
)
1
2
2
3
{({x}^{3})}^{\frac{1}{2}}\sqrt{23}
(x
3
)
2
1
√
23
3 Use this rule:
(
x
a
)
b
=
x
a
b
{({x}^{a})}^{b}={x}^{ab}(xa)b=x
ab
x
322
3{x}^{\frac{3}{2}}\sqrt{23}x2
3√23
4 Regroup terms
23x32
\sqrt{23}{x}^{\frac{3}{2}}
√
23
x23
Answer: √23x 3/2