Question

Simplify. \(\frac{2 m}{3} \cdot 6 m^{2}\)

Short answer

The simplified form of \(\frac{2 m}{3} \cdot 6 m^{2}\) is \(4m^{3}\).

Step-by-step solution

Distinguish the Numerical Coefficients and Variables

The numerical coefficients are \(2/3\) and \(6\), and the variable is \(m\).

Multiply the Numerical Coefficients

Multiply \(2/3\) and \(6\), which gives us \(4\).

Apply the Law of Exponents to the Variables

In \(m \times m^{2}\), apply the law of exponents which states that when multiplying like bases, you add the exponents. Thus, we get \(m^{3}\).