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# Solve the product power $\left(\left(\frac{x^a}{x}\right)^{2a}\left(\left(x^{-121}\right)^a\right)^2\right)^{\frac{1}{a}}$

## Step-by-step Solution

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###  Solution

$x^{\frac{2a^2-244a}{a}}$
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##  Step-by-step Solution 

Problem to solve:

$\left(\left(\frac{x^a}{x}\right)^{2a}\left(\left(x^{-121}\right)^a\right)^2\right)^{\frac{1}{a}}$

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Simplify $\left(\left(x^{-121}\right)^a\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $a$ and $n$ equals $2$

$\left(\left(\frac{x^a}{x}\right)^{2a}x^{-242a}\right)^{\frac{1}{a}}$

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$\left(\left(\frac{x^a}{x}\right)^{2a}x^{-242a}\right)^{\frac{1}{a}}$

Learn how to solve problems step by step online. Solve the product power (((x^a)/x)^(2a)x^(-121)^a^2)^(1/a). Simplify \left(\left(x^{-121}\right)^a\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals a and n equals 2. Simplify the fraction \frac{x^a}{x} by x. Simplify \left(x^{\left(a-1\right)}\right)^{2a} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals a-1 and n equals 2a. Apply the exponent property of product of powers: x^a\cdot x^b=x^{a+b}.

$x^{\frac{2a^2-244a}{a}}$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeFind break even pointsFind the discriminant

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0
a
b
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g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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

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