Question

Use the product of powers property to simplify the expression. $$m \cdot m^{2}$$

Short answer

\(m^{3}\)

Step-by-step solution

Identify the base and exponents

The given expression is \(m \cdot m^{2}\). Here, 'm' is the base and we have two instances of this base. For the first 'm', the exponent is not mentioned, which by default makes it 1 (generically, any number or variable 'n' without an exponent is equivalent to n raised to the power of 1). The exponent for the second 'm' instance is stated as 2.

Apply the product of powers property

Since the base for both parts of the equation is the same, we can combine these by adding the exponents. According to the property of powers, \(m \cdot m^{2}\) can be written as \(m^{1+2}\).

Final Simplification

After adding the exponents, the expression simplifies to \(m^{3}\).