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# Solve the equation with radicals $\sqrt[3]{\sqrt[3]{3^a}}=3^2$

## Step-by-step Solution

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### Videos

$a=18$
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## Step-by-step Solution

Problem to solve:

$\left(\left(3^a\right)^{\frac{1}{3}}\right)^{\frac{1}{3}}=3^2$

Specify the solving method

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Simplify $\sqrt[3]{\sqrt[3]{3^a}}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $\frac{1}{3}$ and $n$ equals $\frac{1}{3}$

$3^{\frac{1}{9}a}=9$

Learn how to solve equations with cubic roots problems step by step online.

$3^{\frac{1}{9}a}=9$

Learn how to solve equations with cubic roots problems step by step online. Solve the equation with radicals 3^a^1/3^1/3=3^2. Simplify \sqrt[3]{\sqrt[3]{3^a}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{3} and n equals \frac{1}{3}. Rewrite the number 9 as a power with base 3 so that we have exponentials with the same base on both sides of the equation. If the bases are the same, then the exponents must be equal to each other. Eliminate the \frac{1}{9} from the left side, multiplying both sides of the equation by the inverse of \frac{1}{9}.

$a=18$
SnapXam A2

### beta Got another answer? Verify it!

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

$\left(\left(3^a\right)^{\frac{1}{3}}\right)^{\frac{1}{3}}=3^2$