What is \sqrt[3x]{m^3}*\sqrt[x]{m^{x-1}} ?

The solution to \sqrt[3x]{m^3}*\sqrt[x]{m^{x-1}} is m

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simplify \sqrt[3x]{m^3}*\sqrt[x]{m^{x-1}}

simplify

3 x m^{3} \cdot x m^{x - 1}

m

Solution steps

3 x m^{3} x m^{x - 1}

3 x m^{3} : m^{\frac{1}{x}}

= m^{\frac{1}{x}} x m^{x - 1}

Apply radical rule:

n a n b = n a \cdot b,

assuming

a \geq 0, b \geq 0

m^{\frac{1}{x}} x m^{x - 1} = (m m^{x - 1})^{\frac{1}{x}}

= (m m^{x - 1})^{\frac{1}{x}}

Simplify

m m^{x - 1} : m^{x}

= (m^{x})^{\frac{1}{x}}

Apply radical rule:

n a^{m} = a^{\frac{m}{n}},

assuming

a \geq 0

= m^{\frac{x}{x}}

Apply rule

\frac{a}{a} = 1

\frac{x}{x} = 1

= m^{1}

Apply rule

a^{1} = a

= m

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1.8 x (10)^{- 3^{^{'}}}

What is \sqrt[3x]{m^3}*\sqrt[x]{m^{x-1}} ?
The solution to \sqrt[3x]{m^3}*\sqrt[x]{m^{x-1}} is m