Simplify the expression $\left(\frac{2x^3y^{-121}}{3y^4}\right)^5$

Step-by-step Solution

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Final answer to the problem

$\left(\frac{2x^3}{3y^{125}}\right)^{4}\frac{5\left(18x^{2}y^{125}-750x^3y^{124}\right)}{9y^{250}}$
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Step-by-step Solution

How should I solve this problem?

  • Solve by implicit differentiation
  • 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
  • Find break even points
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Simplifying

$\frac{d}{dx}\left(\left(\frac{2x^3}{3y^{125}}\right)^5\right)$

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$\frac{d}{dx}\left(\left(\frac{2x^3}{3y^{125}}\right)^5\right)$

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Learn how to solve problems step by step online. Simplify the expression ((2x^3y^(-121))/(3y^4))^5. Simplifying. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. The power of a product is equal to the product of it's factors raised to the same power.

Final answer to the problem

$\left(\frac{2x^3}{3y^{125}}\right)^{4}\frac{5\left(18x^{2}y^{125}-750x^3y^{124}\right)}{9y^{250}}$

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Function Plot

Plotting: $\left(\frac{2x^3}{3y^{125}}\right)^{4}\frac{5\left(18x^{2}y^{125}-750x^3y^{124}\right)}{9y^{250}}$

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7
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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

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