Simplify the algebraic expression $\sqrt{\sqrt{3y^3}}\sqrt[3]{\sqrt{3y^3}}$

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Final answer to the problem

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

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  • Solve by quadratic formula (general formula)
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1

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

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

Learn how to solve multiply powers of same base problems step by step online.

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

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Learn how to solve multiply powers of same base problems step by step online. Simplify the algebraic expression (3y^3)^(1/2)^(1/2)(3y^3)^(1/2)^(1/3). Simplify \sqrt{\sqrt{3y^3}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{2} and n equals \frac{1}{2}. Simplify \sqrt[3]{\sqrt{3y^3}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{2} and n equals \frac{1}{3}. When multiplying exponents with same base we can add the exponents. Calculate the power \left(\frac{1}{2}\right)^2.

Final answer to the problem

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

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Function Plot

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

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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

How to improve your answer:

Main Topic: Multiply powers of same base

When multiplying powers of same base we can add the exponents.

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