Simplify Powers: 15^2 × 15^4 Using Exponent Properties

Simplify the following equation:

$15^2\times15^4=$

To solve the problem of simplifying $15^2 \times 15^4$, we will use the rule for multiplying exponents with the same base.

According to the multiplication of powers rule: If $a$ is a real number and $m$ and $n$ are integers, then:

$a^m \times a^n = a^{m+n}$.

Applying this rule to our problem, where the base $a$ is 15, and the exponents $m$ and $n$ are 2 and 4 respectively:

• Step 1: Identify the base and exponents: $15^2$ and $15^4$ have the same base.
• Step 2: Add the exponents: $2 + 4 = 6$.
• Step 3: Simplify the expression using the rule: $15^2 \times 15^4 = 15^{2+4} = 15^6$.

Therefore, the simplified expression is $15^6$.