Simplify (243^2)^(1/10)

${(243^{2})}^{\frac{1}{10}}$

Step 1

Simplify the expression.

Multiply the exponents in ${(243^{2})}^{\frac{1}{10}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$243^{2 (\frac{1}{10})}$

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

$243^{2 \frac{1}{2 (5)}}$

Cancel the common factor.

$243^{2 \frac{1}{2 \cdot 5}}$

Rewrite the expression.

$243^{\frac{1}{5}}$

Rewrite $243$ as $3^{5}$ .

${(3^{5})}^{\frac{1}{5}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3^{5 (\frac{1}{5})}$

Step 2

Cancel the common factor of $5$ .

Cancel the common factor.

$3^{5 (\frac{1}{5})}$

Rewrite the expression.

$3^{1}$

Step 3

Evaluate the exponent.

$3$