Solve the product power $\left(\left(\frac{a}{b}\right)^a\left(\left(\frac{c}{a}\right)^{4m}\right)^{\frac{1}{n}}\right)^{\frac{1}{m}}$

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Final answer to the problem

$\left(\left(\frac{a}{b}\right)^a\left(\frac{c}{a}\right)^{\frac{4m}{n}}\right)^{\frac{1}{m}}$
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Step-by-step Solution

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Simplify $\left(\left(\frac{c}{a}\right)^{4m}\right)^{\frac{1}{n}}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $4m$ and $n$ equals $\frac{1}{n}$

$\left(\left(\frac{a}{b}\right)^a\left(\frac{c}{a}\right)^{4m\left(\frac{1}{n}\right)}\right)^{\frac{1}{m}}$

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

$\left(\left(\frac{a}{b}\right)^a\left(\frac{c}{a}\right)^{4m\left(\frac{1}{n}\right)}\right)^{\frac{1}{m}}$

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Learn how to solve power of a product problems step by step online. Solve the product power ((a/b)^a(c/a)^(4m)^(1/n))^(1/m). Simplify \left(\left(\frac{c}{a}\right)^{4m}\right)^{\frac{1}{n}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 4m and n equals \frac{1}{n}. Multiply the fraction by the term . Any expression multiplied by 1 is equal to itself.

Final answer to the problem

$\left(\left(\frac{a}{b}\right)^a\left(\frac{c}{a}\right)^{\frac{4m}{n}}\right)^{\frac{1}{m}}$

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Function Plot

Plotting: $\left(\left(\frac{a}{b}\right)^a\left(\frac{c}{a}\right)^{\frac{4m}{n}}\right)^{\frac{1}{m}}$

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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: 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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