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

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## Final Answer

$1.580522\sqrt[4]{y^{5}}$
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## Step-by-step Solution

Problem to solve:

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

Specify the solving method

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 $\frac{1}{2}$

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

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

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

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}. Multiply \frac{1}{2} times \frac{1}{2}. Multiply \frac{1}{2} times \frac{1}{3}.

## Final Answer

$1.580522\sqrt[4]{y^{5}}$
SnapXam A2
Answer Assistant

Go!
1
2
3
4
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

### Useful tips on how to improve your answer:

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

### Main topic:

Multiply powers of same base

~ 0.04 s