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Simplify the expression $\left(\frac{y^3}{2}\right)^2+2\left(\frac{y^3}{2}\right)\left(\left(\frac{1}{2y^3}\right)^{\frac{1}{2y^3}}\right)^2$

Step-by-step Solution

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Final Answer

$\frac{y^{6}+4y^3\left(\frac{1}{2y^3}\right)^{\frac{1}{y^3}}}{4}$
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Step-by-step Solution

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Simplify $\left(\left(\frac{1}{2y^3}\right)^{\frac{1}{2y^3}}\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $\frac{1}{2y^3}$ and $n$ equals $2$

$\left(\frac{y^3}{2}\right)^2+2\left(\frac{y^3}{2}\right)\left(\frac{1}{2y^3}\right)^{\frac{2}{2y^3}}$

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$\left(\frac{y^3}{2}\right)^2+2\left(\frac{y^3}{2}\right)\left(\frac{1}{2y^3}\right)^{\frac{2}{2y^3}}$

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Learn how to solve simplification of algebraic expressions problems step by step online. Simplify the expression ((y^3)/2)^2+2(y^3)/2(1/(2y^3))^(1/(2y^3))^2. Simplify \left(\left(\frac{1}{2y^3}\right)^{\frac{1}{2y^3}}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{2y^3} and n equals 2. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. Cancel the fraction's common factor 2. Combine \frac{y^{6}}{4}+2\left(\frac{y^3}{2}\right)\left(\frac{1}{2y^3}\right)^{\frac{1}{y^3}} in a single fraction.

Final Answer

$\frac{y^{6}+4y^3\left(\frac{1}{2y^3}\right)^{\frac{1}{y^3}}}{4}$

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

SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeFind ((y^3)/2)^2+2(y^3)/2 using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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Function Plot

Plotting: $\frac{y^{6}+4y^3\left(\frac{1}{2y^3}\right)^{\frac{1}{y^3}}}{4}$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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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

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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.

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