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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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$a=18$
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##  Step-by-step Solution 

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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 $\frac{1}{3}$

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

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

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

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}. Multiply \frac{1}{3} times \frac{1}{3}. Simplify \sqrt[9]{3^a} 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 \frac{1}{9}. If the bases are the same, then the exponents must be equal to each other.

$a=18$

##  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

Solve for aFind the rootsSolve by factoringSolve by completing the squareSolve by quadratic formulaFind break even pointsFind the discriminant

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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

### Main Topic: Equations with Cubic Roots

Those equations that they degree (greatest exponent) equals 3.

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