Solve for x (m^(5/6))(m^(1/6))^7=m^x

$(m^{\frac{5}{6}}) {(m^{\frac{1}{6}})}^{7} = m^{x}$

Rewrite the equation as $m^{x} = (m^{\frac{5}{6}}) {(m^{\frac{1}{6}})}^{7}$ .

$m^{x} = (m^{\frac{5}{6}}) {(m^{\frac{1}{6}})}^{7}$

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

$m^{x} = m^{\frac{5}{6}} m^{\frac{1}{6} \cdot 7}$

Multiply $m^{\frac{5}{6}}$ by $m^{\frac{1}{6} \cdot 7}$ by adding the exponents.

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

$m^{x} = m^{\frac{5}{6} + \frac{1}{6} \cdot 7}$

Combine $\frac{1}{6}$ and $7$ .

$m^{x} = m^{\frac{5}{6} + \frac{7}{6}}$

Combine the numerators over the common denominator.

$m^{x} = m^{\frac{5 + 7}{6}}$

Add $5$ and $7$ .

$m^{x} = m^{\frac{12}{6}}$

Divide $12$ by $6$ .

$m^{x} = m^{2}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x = 2$