1Cademy - Simplifying $$2^5 \cdot 2^9$$ and $$3 \cdot 3^4$$ Using the Product Property

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Exponential Notation in Algebra

Example

Simplifying $2^5 \cdot 2^9$ and $3 \cdot 3^4$ Using the Product Property

Apply the Product Property for Exponents to two expressions with numerical bases.

ⓐ $2^5 \cdot 2^9 = 2^{14}$ : Both factors have base $2$ . Add the exponents: $2^5 \cdot 2^9 = 2^{5+9} = 2^{14}$ .

ⓑ $3 \cdot 3^4 = 3^5$ : The first factor, $3$ , can be written as $3^1$ because any number without a visible exponent is understood to have an exponent of $1$ . Now both factors share the base $3$ : $3^1 \cdot 3^4 = 3^{1+4} = 3^5$ .

Part (b) highlights an important detail: a base written without an exponent implicitly carries an exponent of $1$ , so the Product Property still applies.