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# Simplify the expression $\sqrt[5]{\left(\frac{x^{-\frac{1}{2}}}{x^{\frac{3}{2}}}\right)^{2}}$

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##  Final answer to the problem

$\frac{1}{\sqrt[5]{x^{4}}}$
Got another answer? Verify it here!

##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Write in simplest form
• Solve by quadratic formula (general formula)
• Find the derivative using the definition
• Simplify
• Find the integral
• Find the derivative
• Factor
• Factor by completing the square
• Find the roots
Can't find a method? Tell us so we can add it.
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Divide $3$ by $2$

$\sqrt[5]{\left(\frac{x^{-\frac{1}{2}}}{\sqrt{x^{3}}}\right)^{2}}$

Learn how to solve simplification of algebraic expressions problems step by step online.

$\sqrt[5]{\left(\frac{x^{-\frac{1}{2}}}{\sqrt{x^{3}}}\right)^{2}}$

Learn how to solve simplification of algebraic expressions problems step by step online. Simplify the expression ((x^(-1/2))/(x^(3/2)))^2/5. Divide 3 by 2. Divide -1 by 2. Simplify the fraction \frac{x^{-\frac{1}{2}}}{\sqrt{x^{3}}} by x. Simplify \sqrt[5]{\left(x^{-2}\right)^{2}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals -2 and n equals \frac{2}{5}.

##  Final answer to the problem

$\frac{1}{\sqrt[5]{x^{4}}}$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

###  Main Topic: Simplification of algebraic expressions

The simplification of algebraic expressions consists in rewriting a long and complex expression in an equivalent, but much simpler expression. This simplification can be accomplished through the combined use of arithmetic and algebra rules.