Simplify (m^2)^(5/6)*m^(1/3)

${(m^{2})}^{\frac{5}{6}} \cdot m^{\frac{1}{3}}$

Multiply the exponents in ${(m^{2})}^{\frac{5}{6}}$ .

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

$m^{2 (\frac{5}{6})} \cdot m^{\frac{1}{3}}$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$m^{2 \frac{5}{2 (3)}} \cdot m^{\frac{1}{3}}$

Cancel the common factor.

$m^{2 \frac{5}{2 \cdot 3}} \cdot m^{\frac{1}{3}}$

Rewrite the expression.

$m^{\frac{5}{3}} \cdot m^{\frac{1}{3}}$

Multiply $m^{\frac{5}{3}}$ by $m^{\frac{1}{3}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$m^{\frac{5}{3} + \frac{1}{3}}$

Combine the numerators over the common denominator.

$m^{\frac{5 + 1}{3}}$

Add $5$ and $1$ .

$m^{\frac{6}{3}}$

Divide $6$ by $3$ .

$m^{2}$