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Simplify the quotient of powers $\frac{x^4}{\left(x^2+x^3\right)^2}$

Step-by-step Solution

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Final answer to the problem

$\frac{1}{\left(1+x\right)^2}$
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Step-by-step Solution

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Factor the polynomial $\left(x^2+x^3\right)$ by it's greatest common factor (GCF): $x^2$

$\frac{x^4}{\left(x^2\left(1+x\right)\right)^2}$

Learn how to solve quotient of powers problems step by step online.

$\frac{x^4}{\left(x^2\left(1+x\right)\right)^2}$

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Learn how to solve quotient of powers problems step by step online. Simplify the quotient of powers (x^4)/((x^2+x^3)^2). Factor the polynomial \left(x^2+x^3\right) by it's greatest common factor (GCF): x^2. The power of a product is equal to the product of it's factors raised to the same power. Simplify \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 2. Multiply 2 times 2.

Final answer to the problem

$\frac{1}{\left(1+x\right)^2}$

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Function Plot

Plotting: $\frac{1}{\left(1+x\right)^2}$

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0
a
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g
m
n
u
v
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x
y
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.
(◻)
+
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◻/◻
/
÷
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

How to improve your answer:

Main Topic: Quotient of Powers

The quotient of powers of same base is equivalent to the same base to the power of the difference of exponents: $\frac{a^m}{a^n}=a^{m-n}$.

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