Solve the product power $\sqrt{\left(3^{\left(x^2\right)}\right)^{xy}\left(3^{\left(y^2\right)}\right)^{xy}}$

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Final answer to the problem

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

$\sqrt{3^{x^2xy}\left(3^{\left(y^2\right)}\right)^{xy}}$

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$\sqrt{3^{x^2xy}\left(3^{\left(y^2\right)}\right)^{xy}}$

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

Final answer to the problem

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

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

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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

How to improve your answer:

Main Topic: Power of a product

The power of a product of factors is equal to the product of each factor to the same power: $\left(b\cdot c\right)^n=b^n\cdot c^n$.

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