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Solve the product power $\sqrt[6]{81a^{24}b^{12}c^8}$

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Solution

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Final answer to the problem

$\sqrt[6]{81}a^{4}b^{2}\sqrt[3]{c^{4}}$
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Step-by-step Solution

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The power of a product is equal to the product of it's factors raised to the same power

$\sqrt[6]{81}a^{4}\sqrt[6]{b^{12}}\sqrt[6]{c^8}$

Learn how to solve power of a product problems step by step online.

$\sqrt[6]{81}a^{4}\sqrt[6]{b^{12}}\sqrt[6]{c^8}$

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Learn how to solve power of a product problems step by step online. Solve the product power (81a^24b^12c^8)^(1/6). The power of a product is equal to the product of it's factors raised to the same power. The power of a product is equal to the product of it's factors raised to the same power. Simplify \sqrt[6]{a^{24}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 24 and n equals \frac{1}{6}. Multiply the fraction and term in 24\cdot \left(\frac{1}{6}\right).

Final answer to the problem

$\sqrt[6]{81}a^{4}b^{2}\sqrt[3]{c^{4}}$

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Function Plot

Plotting: $\sqrt[6]{81}a^{4}b^{2}\sqrt[3]{c^{4}}$

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7
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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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:

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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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